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

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

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

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

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.

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

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

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:

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.

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.

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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.

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.

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

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.

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

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.

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

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

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

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

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.

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 $\mathit{CAT}(0)$

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.

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

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

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

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

In this paper, we propose two strongly convergent algorithms which combines diagonal subgradient method, projection method and proximal method to solve split equilibrium problems and split common fixed point problems of nonexpansive mappings in a real Hilbert space: fixed point set constrained split equilibrium problems (FPSCSEPs) in real Hilbert spaces. The computations of first algorthim requires

In this paper, motivated and inspired by Samet et al., we introduce the notion of generalized weakly contractive mappings in metric spaces and prove the existence and uniqueness of fixed point for such mappings, and we obtain a coupled fixed point theorem in metric spaces. These theorems generalize many previously obtained fixed point results. An example is given to illustrate the main result. Finally

In the publication of this article [Fixed Point Theory Appl. 2017:26, 2017], there is an error in Section 3. The error: Corollary 3.22 Let $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter $s \ge 1$ , and let f, g be two self-maps of X with $\psi \in \Psi $ , $\varphi \in \Phi $ satisfying the condition $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl(

In 1980, Hegedüs and Szilágyi proved some fixed point theorem in complete metric spaces. Introducing a new contractive condition, we generalize Hegedüs-Szilágyi’s fixed point theorem. We discuss the relationship between the new contractive condition and other contractive conditions. We also show that we cannot extend Hegedüs-Szilágyi’s fixed point theorem to Meir-Keeler type.

In this paper, we establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Our results generalize and extend the results of Joseph et al. (SpringerPlus 5:Article ID 217, 2016). We also give examples to support our results, and applications relating the results to a fixed point for multivalued mappings and fuzzy mappings are studied.

This work is for giving the probabilistic aspect to the known b-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2):263-276, 1998), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.