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New Tseng’s extragradient methods for pseudomonotone variational inequality problems in Hadamard manifolds Fixed Point Theory Appl. Pub Date : 2021-02-22 Konrawut Khammahawong; Poom Kumam; Parin Chaipunya; Somyot Plubtieng
We propose Tseng’s extragradient methods for finding a solution of variational inequality problems associated with pseudomonotone vector fields in Hadamard manifolds. Under standard assumptions such as pseudomonotone and Lipschitz continuous vector fields, we prove that any sequence generated by the proposed methods converges to a solution of variational inequality problem, whenever it exits. Moreover
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Common fixed point for some generalized contractive mappings in a modular metric space with a graph Fixed Point Theory Appl. Pub Date : 2021-02-08 Karim Chaira; Abderrahim Eladraoui; Mustapha Kabil; Abdessamad Kamouss
In this paper, we investigate the existence and the uniqueness of a common fixed point of a pair of self-mappings satisfying new contractive type conditions on a modular metric space endowed with a reflexive digraph. An application is given to show the use of our main result.
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On Berinde’s method for comparing iterative processes Fixed Point Theory Appl. Pub Date : 2021-02-01 Constantin Zălinescu
In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl. 2:97–105, 2004) because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde
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A fixed point theorem for generalized \((\psi ,\varphi )\)-weak contractions in Branciari type generalized metric spaces Fixed Point Theory Appl. Pub Date : 2021-01-25 Zhiqun Xue; Guiwen Lv
In this paper, we obtain a new convergence theorem for fixed points of weak contractions in Branciari type generalized metric spaces under weaker conditions. The proof process of the theorem is new and different from that of other authors. An illustrative example of this theorem is to show how the new conditions extend known results.
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Minimal set of periods for continuous self-maps of the eight space Fixed Point Theory Appl. Pub Date : 2021-01-18 Jaume Llibre; Ana Sá
Let $G_{k}$ be a bouquet of circles, i.e., the quotient space of the interval $[0,k]$ obtained by identifying all points of integer coordinates to a single point, called the branching point of $G_{k}$ . Thus, $G_{1}$ is the circle, $G_{2}$ is the eight space, and $G_{3}$ is the trefoil. Let $f: G_{k} \to G_{k}$ be a continuous map such that, for $k>1$ , the branching point is fixed. If $\operatorname{Per}(f)$
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The iterative solutions of split common fixed point problem for asymptotically nonexpansive mappings in Banach spaces Fixed Point Theory Appl. Pub Date : 2020-12-08 Yuanheng Wang; Xiuping Wu; Chanjuan Pan
In this paper, we propose an iteration algorithm for finding a split common fixed point of an asymptotically nonexpansive mapping in the frameworks of two real Banach spaces. Under some suitable conditions imposed on the sequences of parameters, some strong convergence theorems are proved, which also solve some variational inequalities that are closely related to optimization problems. The results
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Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces Fixed Point Theory Appl. Pub Date : 2020-11-09 Noureddine El Harmouchi; Karim Chaira; El Miloudi Marhrani
In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.
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Fixed point results for Geraghty quasi-contraction type mappings in dislocated quasi-metric spaces Fixed Point Theory Appl. Pub Date : 2020-11-02 Joy C. Umudu; Johnson O. Olaleru; Adesanmi A. Mogbademu
In this paper, fixed point results for a newly introduced Geraghty quasi-contraction type mappings are proved in more general metric spaces called T-orbitally complete dislocated quasi-metric spaces. Geraghty quasi-contraction type mappings generalize, among others, Ciric’s quasi-contraction mappings and other Geraghty quasi-contractive type mappings in the literature. Fixed point results are obtained
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A short and sharpened way to approach fixed point results involving fuzzy \(\mathcal{H}\)-contractive mappings Fixed Point Theory Appl. Pub Date : 2020-10-01 Hayel N. Saleh; Mohammad Imdad; Md Hasanuzzaman
In the present paper, we adopt a short and sharpened approach to prove fixed point results involving fuzzy $\mathcal{H}$ -contractive mappings utilized in (Wardowski, Fuzzy Sets Syst. 125:245–252, 2013) and other related articles. In this process, we are able to relax some conditions utilized by earlier authors which in turn yields affirmative answers to some open questions raised by earlier authors
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K-Correspondences, USCOs, and fixed point problems arising in discounted stochastic games Fixed Point Theory Appl. Pub Date : 2020-09-22 Frank H. Page; Jing Fu
We establish a fixed point theorem for the composition of nonconvex, measurable selection valued correspondences with Banach space valued selections. We show that if the underlying probability space of states is nonatomic and if the selection correspondences in the composition are K-correspondences (meaning correspondences having graphs that contain their Komlos limits), then the induced measurable
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Strong convergence of an inertial algorithm for maximal monotone inclusions with applications Fixed Point Theory Appl. Pub Date : 2020-08-21 C. E. Chidume; A. Adamu; M. O. Nnakwe
An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem proved is applied to approximate a solution of a convex optimization problem and a solution of a Hammerstein
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A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications Fixed Point Theory Appl. Pub Date : 2020-08-01 Charles E. Chidume; Poom Kumam; Abubakar Adamu
An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore
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Common fixed point theorems for two and three mappings Fixed Point Theory Appl. Pub Date : 2020-07-20 Meryeme El Harrak; Ahmed Hajji
In this paper, we provide common fixed point theorems for two and three commuting mappings which generalize Darbo’s fixed point theorem. An explicit example is given for illustration.
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Some perturbation results of Kirchhoff type equations via Morse theory Fixed Point Theory Appl. Pub Date : 2020-07-13 Mingzheng Sun; Yutong Chen; Rushun Tian
In this paper, we consider the following Kirchhoff type equation: $$ \textstyle\begin{cases} - (a+b \int _{\varOmega } \vert \nabla u \vert ^{2}\,dx ) \Delta u= f(x,u) &\text{in } \varOmega , \\ u=0 &\text{on } \partial \varOmega , \end{cases} $$ where $a,b>0$ are constants and $\varOmega \subset \mathbb{R}^{N}$ ( $N=1,2,3$ ) is a bounded domain with smooth boundary ∂Ω. By applying Morse theory, we
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A self-adaptive inertial subgradient extragradient method for pseudomonotone equilibrium and common fixed point problems Fixed Point Theory Appl. Pub Date : 2020-07-06 Lateef Olakunle Jolaoso; Maggie Aphane
In this paper, we introduce a self-adaptive inertial subgradient extragradient method for solving pseudomonotone equilibrium problem and common fixed point problem in real Hilbert spaces. The algorithm consists of an inertial extrapolation process for speeding the rate of its convergence, a monotone nonincreasing stepsize rule, and a viscosity approximation method which guaranteed its strong convergence
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On monotone nonexpansive mappings in \(\operatorname{CAT}_{p}(0)\) spaces Fixed Point Theory Appl. Pub Date : 2020-07-01 Sami Shukri
In this paper, based on some geometrical properties of $\operatorname{CAT}_{p}(0)$ spaces, for $p \geq 2$, we obtain two fixed point results for monotone multivalued nonexpansive mappings and proximally monotone nonexpansive mappings. Which under some assumptions, reduce to coincide and generalize a fixed point result for monotone nonexpansive mappings. This work is a continuity of the previous work
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Related Suzuki-type fixed point theorems in ordered metric space Fixed Point Theory Appl. Pub Date : 2020-06-01 Outass Rida; Chaira Karim; Marhrani El Miloudi
In this paper, we use Suzuki-type contraction to prove three fixed point theorems for generalized contractions in an ordered space equipped with two metrics; we obtain some generalizations of the Kannan fixed point theorem. Our results on partially ordered metric spaces generalize and extend some results of Ran and Reurings as well as of Nieto and Rodríguez-López. To illustrate the effectiveness of
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Set-valued Leader type contractions, periodic point and endpoint theorems, quasi-triangular spaces, Bellman and Volterra equations Fixed Point Theory Appl. Pub Date : 2020-03-24 Kazimierz Włodarczyk
Set-valued contractions of Leader type in quasi-triangular spaces are constructed, conditions guaranteeing the existence of nonempty sets of periodic points, fixed points and endpoints of such contractions are established, convergence of dynamic processes of these contractions are studied, uniqueness properties are derived, and single-valued cases are considered. Investigated dynamic systems are not
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Retraction Note: Fixed point theorems and explicit estimates for convergence rates of continuous time Markov chains Fixed Point Theory Appl. Pub Date : 2020-02-27 Zhenhai Yan; Guojun Yan; Ikudol Miyamoto
The Editors-in-Chief have retracted this article [1] because it showed evidence of peer review manipulation. In addition, the identity of the corresponding author could not be verified: Nagoya University have confirmed that Ikudol Miyamato has not been affiliated with their Graduate School of Mathematics. The authors have not responded to any correspondence regarding this retraction.
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Iterative algorithms for solutions of Hammerstein equations in real Banach spaces Fixed Point Theory Appl. Pub Date : 2020-02-17 Charles E. Chidume; Abubakar Adamu; Lois C. Okereke
Let B be a uniformly convex and uniformly smooth real Banach space with dual space $B^{*}$. Let $F:B\to B^{*}$, $K:B^{*} \to B$ be maximal monotone mappings. An iterative algorithm is constructed and the sequence of the algorithm is proved to converge strongly to a solution of the Hammerstein equation $u+KFu=0$. This theorem is a significant improvement of some important recent results which were proved
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New algorithms for approximating zeros of inverse strongly monotone maps and J-fixed points Fixed Point Theory Appl. Pub Date : 2020-01-31 Charles E. Chidume; Chinedu G. Ezea
Let E be a real Banach space with dual space $E^{*}$. A new class of relatively weakJ-nonexpansive maps, $T:E\rightarrow E^{*}$, is introduced and studied. An algorithm to approximate a common element of J-fixed points for a countable family of relatively weak J-nonexpansive maps and zeros of a countable family of inverse strongly monotone maps in a 2-uniformly convex and uniformly smooth real Banach
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Retraction Note: Sharp geometrical properties of a-rarefied sets via fixed point index for the Schrödinger operator equations Fixed Point Theory Appl. Pub Date : 2020-01-28 Zhiqiang Li; Beatriz Ychussie
The Editors-in-Chief have retracted this article [1] because it overlaps significantly with a number of previously published articles from different authors [2-4] and one article by different authors that was simultaneously under consideration with another journal [5]. The article also showed evidence of peer review manipulation. Additionally, the identity of the corresponding author could not be verified:
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Retraction Note: Fixed point theorems for solutions of the stationary Schrödinger equation on cones Fixed Point Theory Appl. Pub Date : 2020-01-22 Gaixian Xue; Eve Yuzbasi
The Editors-in-Chief have retracted this article [1] because the results presented are invalid. The article also shows significant overlap with a number of previously published articles [2–5] and evidence of both peer review and authorship manipulation. The authors have not responded to any correspondence regarding this retraction.
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A best proximity point theorem for special generalized proximal β-quasi contractive mappings Fixed Point Theory Appl. Pub Date : 2019-12-02 M. Iadh Ayari; M. M. M. Jaradat; Z. Mustafa
In this paper, we obtain some best proximity point results for a new class of non-self mappings $T:A \longrightarrow B$ called special generalized proximal β-quasi contractive. Our result is illustrated by an example. Several consequences are derived.
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Ordered \(S_{p}\)-metric spaces and some fixed point theorems for contractive mappings with application to periodic boundary value problems Fixed Point Theory Appl. Pub Date : 2019-11-01 Z. Mustafa; R. J. Shahkoohi; V. Parvaneh; Z. Kadelburg; M. M. M. Jaradat
In this paper, we introduce the structure of $S_{p}$ -metric spaces as a generalization of both S-metric and $S_{b}$ -metric spaces. Also, we present the notions of S̃-contractive mappings in the setup of ordered $S_{p}$ -metric spaces and investigate the existence of a fixed point for such mappings under various contractive conditions. We provide examples to illustrate the results presented herein
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Random fixed point theorems in Banach spaces applied to a random nonlinear integral equation of the Hammerstein type Fixed Point Theory Appl. Pub Date : 2019-10-01 Godwin Amechi Okeke; Sheila Amina Bishop; Hudson Akewe
The purpose of this paper is to define a new random operator called the generalized ϕ-weakly contraction of the rational type. This new random operator includes those studied by Khan et al. (Filomat 31(12):3611–3626, 2017) and Zhang et al. (Appl. Math. Mech. 32(6):805–810, 2011) as special cases. We prove some convergence, existence, and stability results in separable Banach spaces. Moreover, we produce
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Gap functions and error bounds for vector inverse mixed quasi-variational inequality problems Fixed Point Theory Appl. Pub Date : 2019-09-01 Zhong-bao Wang; Zhang-you Chen; Zhe Chen
This paper is devoted to investigating a vector inverse mixed quasi-variational inequality (VIMQVI). Our aim is to obtain error bounds for VIMQVI in terms of different gap functions, i.e., the residual gap function, the regularized gap function, and the D-gap function. These bounds provide effective estimated distances between an arbitrary feasible point and the solution set of VIMQVI. The approach
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F-contractive type mappings in b-metric spaces and some related fixed point results Fixed Point Theory Appl. Pub Date : 2019-08-01 Nilakshi Goswami; Nehjamang Haokip; Vishnu Narayan Mishra
In this paper, we define F-contractive type mappings in b-metric spaces and prove some fixed point results with suitable examples. F-expanding type mappings are also defined and a fixed point result is obtained.
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Relation-theoretic coincidence and common fixed point results under \((F,\mathcal{R})_{g}\)-contractions with an application Fixed Point Theory Appl. Pub Date : 2019-07-01 Waleed M. Alfaqih; Mohammad Imdad; Rqeeb Gubran; Idrees A. Khan
In this paper, we begin with some observations on F-contractions. Thereafter, we introduce the notion of $(F,\mathcal{R})_{g}$ -contractions and utilize the same to prove some coincidence and common fixed point results in the setting of metric spaces endowed with binary relations. An example is also given to exhibit the utility of our results. We also deduce some consequences in the setting of ordered
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A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications Fixed Point Theory Appl. Pub Date : 2019-06-17 C. E. Chidume; M. O. Nnakwe; A. Adamu
Let X be a uniformly convex and uniformly smooth real Banach space with dual space $X^{*}$ . In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex optimization problem
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A best proximity point theorem for α-proximal Geraghty non-self mappings Fixed Point Theory Appl. Pub Date : 2019-06-03 Mohamed Iadh Ayari
In this paper, we search some best proximity point results for a new class of non-self mappings $T:A \longrightarrow B$ called α-proximal Geraghty mappings. Our results extend many recent results appearing in the literature. We suggest an example to support our result. Several consequences are derived. As applications, we investigate the existence of best proximity points for a metric space endowed
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On algebraic properties of soft real points Fixed Point Theory Appl. Pub Date : 2019-05-20 Sabir Hussain; Hurmet Fulya Akiz; Amlak Ibrahim Alajlan
In this paper, we introduce and discuss soft single points, which proceed towards soft real points by using real numbers and subsets of set of real numbers. We also define the basic operations on soft real points and explore the algebraic properties. We observe that the set of all soft real points forms a ring. Moreover, we study the soft real point metric using soft real point and explore some of
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Δ-convergence for proximal point algorithm and fixed point problem in CAT(0) spaces Fixed Point Theory Appl. Pub Date : 2019-05-08 Shamshad Husain; Nisha Singh
In this paper, we prove the Δ-convergence of a modified proximal point algorithm for common fixed points in a CAT(0) space for different classes of generalized nonexpansive mappings including a total asymptotically nonexpansive mapping, a multivalued mapping, and a minimizer of a convex function. The results in this paper generalize the corresponding results given by some authors. Moreover, numerical
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Generalization of best proximity points theorem for non-self proximal contractions of first kind Fixed Point Theory Appl. Pub Date : 2019-02-25 Mohamed Iadh Ayari; Zead Mustafa; Mohammed Mahmoud Jaradat
The primary objective of this paper is the study of the generalization of some results given by Basha (Numer. Funct. Anal. Optim. 31:569–576, 2010). We present a new theorem on the existence and uniqueness of best proximity points for proximal β-quasi-contractive mappings for non-self-mappings $S:M\rightarrow N$ and $T:N\rightarrow M$ . Furthermore, as a consequence, we give a new result on the existence
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An inertial S-iteration process Fixed Point Theory Appl. Pub Date : 2019-02-18 Aniruth Phon-on; Nifatamah Makaje; Areeyuth Sama-Ae; Kittiya Khongraphan
In this paper, we establish a new iteration method, called an InerSP (an inertial S-iteration process), by combining a modified S-iteration process with the inertial extrapolation. This strategy is for speeding up the convergence of the algorithm. We then prove the convergence theorems of a sequence generated by our new method for finding a common fixed point of nonexpansive mappings in a Banach space
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Observations on relation-theoretic coincidence theorems under Boyd–Wong type nonlinear contractions Fixed Point Theory Appl. Pub Date : 2019-02-11 Aftab Alam; Mohammad Imdad; Mohammad Arif
In this article, we carry out some observations on existing metrical coincidence theorems of Karapinar et al. (Fixed Point Theory Appl. 2014:92, 2014) and Erhan et al. (J. Inequal. Appl. 2015:52, 2015) proved for Lakshmikantham–Ćirić-type nonlinear contractions involving $(f,g)$ -closed transitive sets after proving some coincidence theorems satisfying Boyd–Wong-type nonlinear contractivity conditions
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The Maslov index and the spectral flow—revisited Fixed Point Theory Appl. Pub Date : 2019-02-04 Marek Izydorek; Joanna Janczewska; Nils Waterstraat
We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators. We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators on a Hilbert space
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Iterative approximation of attractive points of further generalized hybrid mappings in Hadamard spaces Fixed Point Theory Appl. Pub Date : 2019-01-28 Asawathep Cuntavepanit; Withun Phuengrattana
In this paper, we study the class of further generalized hybrid mappings due to Khan (Fixed Point Theory Appl. 2018:8, 2018) in the setting of Hadamard spaces. We prove a demiclosed principle for such mappings in Hadamard spaces. Furthermore, we also prove the Δ-convergence of the sequence generated by the S-iteration process for finding attractive points of further generalized hybrid mappings in Hadamard
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Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions Fixed Point Theory Appl. Pub Date : 2019-01-21 M. Kamenskii; V. Obukhovskii; G. Petrosyan; Jen-Chih Yao
We study a semilinear fractional order differential inclusion in a separable Banach space E of the form $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where ${}^{C}D^{q}$ is the Caputo fractional derivative of order $0 < q < 1$ , $A \colon D(A) \subset E \rightarrow E$ is a generator of a $C_{0}$ -semigroup, and $F \colon [0,T] \times E \multimap E$ is a nonlinear multivalued
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Bernstein-type theorem for ϕ-Laplacian Fixed Point Theory Appl. Pub Date : 2019-01-07 Jakub Maksymiuk; Jakub Ciesielski; Maciej Starostka
In this paper we obtain a solution to the second-order boundary value problem of the form $\frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u})$ , $t\in [0,1]$ , $u\colon \mathbb {R}\to \mathbb {R}$ with Sturm–Liouville boundary conditions, where $\varPhi\colon \mathbb {R}\to \mathbb {R}$ is a strictly convex, differentiable function and $f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R}$ is
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Fixed point theorems in a new type of modular metric spaces Fixed Point Theory Appl. Pub Date : 2018-12-01 Duran Turkoglu; Nesrin Manav
In this paper, considering both a modular metric space and a generalized metric space in the sense of Jleli and Samet (Fixed Point Theory Appl. 2015:61, 2015), we introduce a new concept of generalized modular metric space. Then we present some examples showing that the generalized modular metric space includes some kind of metric structures. Finally, we provide some fixed point results for both contraction
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Application of the Brouwer and the Kakutani fixed-point theorems to a discrete equation with a double singular structure Fixed Point Theory Appl. Pub Date : 2018-11-01 Minoru Tabata; Nobuoki Eshima
Applying the method consisting of a combination of the Brouwer and the Kakutani fixed-point theorems to a discrete equation with a double singular structure, that is, to a discrete singular equation of which the denominator contains another discrete singular operator, we prove that the equation has a solution.
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On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications Fixed Point Theory Appl. Pub Date : 2018-10-15 Ning Ruan; David Yang Gao
This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e., the general fixed point problem is first reformulated as a nonconvex optimization problem, its well-posedness is discussed based on the objectivity principle in continuum physics; then the canonical duality theory is applied for solving this challenging problem
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\(F(\psi,\varphi)\)-Contractions for α-admissible mappings on M-metric spaces Fixed Point Theory Appl. Pub Date : 2018-10-01 Hossein Monfared; Mehdi Asadi; Mahdi Azhini; Donal O’Regan
In this paper, we introduce certain α-admissible mappings which are $F(\psi,\varphi)$ -contractions on M-metric spaces, and we establish some fixed point results. Our results generalize and extend some well-known results on this topic in the literature.
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Caristi type cyclic contraction and common fixed point theorems in bipolar metric spaces with applications Fixed Point Theory Appl. Pub Date : 2018-09-17 G. N. V. Kishore; Ravi P. Agarwal; B. Srinuvasa Rao; R. V. N. Srinivasa Rao
In this paper, we obtain the existence and uniqueness of the solution for three self mappings in a complete bipolar metric space under a new Caristi type contraction with an example. We also provide applications to homotopy theory and nonlinear integral equations.
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Boundary value problems for singular second order equations Fixed Point Theory Appl. Pub Date : 2018-09-03 Alessandro Calamai; Cristina Marcelli; Francesca Papalini
We investigate strongly nonlinear differential equations of the type $$\bigl(\Phi \bigl(k(t) u'(t) \bigr) \bigr)'= f \bigl(t,u(t),u'(t) \bigr), \quad\text{a.e. on } [0,T], $$ where Φ is a strictly increasing homeomorphism and the nonnegative function k may vanish on a set of measure zero. By using the upper and lower solutions method, we prove existence results for the Dirichlet problem associated
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Some results on fixed point theory for a class of generalized nonexpansive mappings Fixed Point Theory Appl. Pub Date : 2018-08-13 Bijoy Patir; Nilakshi Goswami; Vishnu Narayan Mishra
In this paper, we introduce a new class of generalized nonexpansive mappings which is wider than the class of mappings satisfying (C) condition. Different properties and some fixed point results for these mappings are obtained here. The convergence of some iteration schemes to the fixed point is also discussed with suitable examples.
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Best proximity point results for Hardy–Rogers p-proximal cyclic contraction in uniform spaces Fixed Point Theory Appl. Pub Date : 2018-08-06 Victoria O. Olisama; Johnson O. Olaleru; Hudson Akewe
The Hardy–Rogers p-proximal cyclic contraction, which includes the cyclic, Kannan, Chatterjea and Reich contractions as sub-classes, is developed in uniform spaces. The existence and uniqueness results of best proximity points for these contractions are proved. The results, which are for non-self maps, apart from the fact that they are new in literature, generalise several other similar results in
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Common fixed point theorems for a finite family of multivalued mappings in an ordered Banach space Fixed Point Theory Appl. Pub Date : 2018-06-25 Mohamed Amine Farid; Karim Chaira; El Miloudi Marhrani; Mohamed Aamri
In this paper, we prove some common fixed point theorems for a finite family of multivalued and single-valued mappings operating on ordered Banach spaces. Our results extend and generalize many results in the literature on fixed point theory and lead to existence theorems for a system of integral inclusions.
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Convergence theorems of subgradient extragradient algorithm for solving variational inequalities and a convex feasibility problem Fixed Point Theory Appl. Pub Date : 2018-06-18 C. E. Chidume; M. O. Nnakwe
Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space $E^{*}$ . In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively nonexpansive maps. The theorems
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Halpern–Ishikawa type iterative method for approximating fixed points of non-self pseudocontractive mappings Fixed Point Theory Appl. Pub Date : 2018-06-04 Habtu Zegeye; Abebe Regassa Tufa
In this paper, we define a Halpern–Ishikawa type iterative method for approximating a fixed point of a Lipschitz pseudocontractive non-self mapping T in a real Hilbert space settings and prove strong convergence result of the iterative method to a fixed point of T under some mild conditions. We give a numerical example to support our results. Our results improve and generalize most of the results that
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The split common fixed point problem for infinite families of demicontractive mappings Fixed Point Theory Appl. Pub Date : 2018-05-28 Adisak Hanjing; Suthep Suantai
In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong convergence of the proposed method is established under suitable control conditions. We apply our main results to study the split common null point problem, the split variational inequality problem, and the split equilibrium problem in the framework of
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Fixed point theorems for a class of generalized weak cyclic compatible contractions Fixed Point Theory Appl. Pub Date : 2018-05-07 P. S. Kumari; J. Nantadilok; M. Sarwar
In this manuscript, we establish a coincidence point and a unique common fixed point theorem for $(\psi ,\varphi )$ -weak cyclic compatible contractions. We also present a fixed point theorem for a class of Λ-weak cyclic compatible contractions via altering distance functions. Our results extend and improve some well-known results in the literature. We provide examples to analyze and illustrate our
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Infinitely split Nash equilibrium problems in repeated games Fixed Point Theory Appl. Pub Date : 2018-04-23 Jinlu Li
In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in (J. Math. Anal. Appl. 409:1084–1092, 2014), we prove an existence theorem. As an application, we study the repeated extended Bertrant duopoly model of price competition.
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Some convergence results using K iteration process in \(\mathit{CAT}(0)\) spaces Fixed Point Theory Appl. Pub Date : 2018-04-16 Kifayat Ullah; Kashif Iqbal; Muhammad Arshad
In this paper, some strong and Δ-convergence results are proved for Suzuki generalized nonexpansive mappings in the setting of $\mathit{CAT}(0)$ spaces using the K iteration process. We also give an example to show the efficiency of the K iteration process. Our results are the extension, improvement and generalization of many well-known results in the literature of fixed point theory in $\mathit{CAT}(0)$
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Axiom of Infinite Choice, transversal ordered spring spaces and fixed points Fixed Point Theory Appl. Pub Date : 2018-04-02 Milan R. Tasković
This paper continues the study of the Axiom of Infinite Choice on transversal ordered spring spaces in terms of fixed point and increasing inductive sets. These principles unify a number of diverse results (about three thousand papers) in fixed point theory, especially recently published. Applications in partially ordered spaces and fixed point theory are also considered.
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Inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps Fixed Point Theory Appl. Pub Date : 2018-03-12 C. E. Chidume; S. I. Ikechukwu; A. Adamu
In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly convex and uniformly smooth real Banach space. We prove a strong convergence theorem. This theorem is an improvement of the result of Matsushita and Takahashi (J. Approx. Theory 134:257–266, 2005) and the result of Dong et al. (Optim. Lett. 12:87–102
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Iterative approximation of common attractive points of further generalized hybrid mappings Fixed Point Theory Appl. Pub Date : 2018-03-05 Safeer Hussain Khan
Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl. 2013:69, 2013, https://doi
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On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings Fixed Point Theory Appl. Pub Date : 2018-03-01 Withun Phuengrattana; Kritsada Lerkchaiyaphum
We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our results improve and
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Fixed points of fuzzy neutrosophic soft mapping with decision-making Fixed Point Theory Appl. Pub Date : 2018-02-19 Muhammad Riaz; Masooma Raza Hashmi
In this paper, we introduce some operations on a fuzzy neutrosophic soft set ( $\mathfrak{fns}$ -set) by utilizing the theories of fuzzy sets, soft sets and neutrosophic sets. We introduce $\mathfrak{fns}$ -mappings by using a cartesian product with relations on $\mathfrak{fns}$ -sets and establish some results on fixed points of an $\mathfrak{fns}$ -mapping. We present an algorithm to deal with uncertainties
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