• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-22
Rafael Espínola-García, María Japón, Daniel Souza

The purpose of this work is two-fold. On the one side, we focus on the space of real convergent sequences c where we study non-weakly compact sets with the fixed point property. Our approach brings a positive answer to a recent question raised by Gallagher et al. in (J Math Anal Appl 431(1):471–481, 2015). On the other side, we introduce a new metric structure closely related to the notion of relative

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-20
Qiao-Li Dong, Xiao-Huan Li, Yeol Je Cho, Themistocles M. Rassias

Recently, the authors (Dong et al. in J Global Optim 73(4):801–824, 2019) introduced the multi-step inertial Krasnosel’skiǐ–Mann iteration, where the inertial parameters involve the iterative sequence. Therefore, one has to compute the inertial parameters per iteration. The aim of this article is to present two kinds of inertial parameter arrays which do not depend on the iterative sequence. We first

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-18
Houwang Li, Wenming Zou

In the present paper, we study the normalized solutions with least energy to the following system: \begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+\lambda _1u=\mu _1 |u|^{p-2}u+\beta r_1|u|^{r_1-2}|v|^{r_2}u\quad &{}\hbox {in}~{{\mathbb {R}}^N},\\ -\Delta v+\lambda _2v=\mu _2 |v|^{q-2}v+\beta r_2|u|^{r_1}|v|^{r_2-2}v\quad &{}\hbox {in}~{{\mathbb {R}}^N},\\ \int _{{{\mathbb {R}}^N}}u^2=a_1^2\quad • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-17 M. Gabeleh, J. Markin Recent work by Lau and Yao (J Math Anal Appl 459:203–216, 2018) and Mohamadi (J Fixed Point Theory Appl 21:83, 2019) initiated the study of common fixed points for commuting families of multivalued mappings. Working in locally convex linear spaces the authors assumed that the mappings are convex with the exception that Mohamadi established a common fixed point result for non-convex mappings in one-dimensional • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-15 Xue-ping Luo In this paper, a new class of set-valued inverse variational inequalities (SIVIs) are introduced and investigated in reflexive Banach spaces. Several equivalent characterizations are given for the set-valued inverse variational inequality to have a nonempty and bounded solution set. Based on the equivalent condition, we propose the stability result for the set-valued inverse variational inequality • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-13 T. Domínguez Benavides, P. Lorenzo Ramírez This paper is devoted to state some fixed point results for multivalued mappings in modular vector spaces. For this purpose, we study the uniform noncompact convexity, a geometric property for modular spaces which is similar to nearly uniform convexity in the Banach spaces setting. Using this property, we state several new fixed point theorems for multivalued nonexpansive mappings in modular spaces • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-07-12 Shiping Lu, Shile Zhou, Xingchen Yu In this paper, the problems of existence, non-existence, and uniqueness of homoclinic solutions are studied for relativistic Liénard equations:\begin{aligned} \left( \frac{x'}{\sqrt{1-\frac{x'^{2}}{\nu ^{2}}}}\right) '+f(x)x'+g(t,x)=p(t), \end{aligned}$$where $$\nu >0$$ is a constant, $$f\in C({\mathbb {R}},{\mathbb {R}}), g\in C({\mathbb {R}}\times {\mathbb {R}},{\mathbb {R}})$$ with $$T-$$periodic • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-06-29 M. Y. Abdallah, A. Al-Izeri, K. Latrach In this paper, we present several fixed set theorems for multivalued mappings in Banach spaces, which in turn are multivalued versions of the Krasnosel’skii fixed point theorem, for various kind of perturbations. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-06-12 Mecheraoui Rachid, Zoran D. Mitrović, Vahid Parvaneh, Zohreh Bagheri The main purpose of this paper is to show that the Meir–Keeler contraction principle, as well as some of its generalizations, is, in general, not true in quasi-metric spaces. After that, we suggest a new Meir–Keeler type contraction that guaranties the existence and uniqueness of fixed points in quasi-metric spaces. Finally, to illustrate the wide usability of our findings, we discuss the existence • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-06-11 Sergey A. Timoshin, Alexander A. Tolstonogov This paper addresses an evolution inclusion of subdifferential type with a multivalued perturbation. The values of the latter are closed, not necessarily convex sets. Our inclusion is implicit in the sense that the velocity enters it implicitly: the subdifferential is evaluated not at the state, but at a function depending both on the state and the velocity. We prove the existence of a solution to • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-06-11 Adrian Petruşel, Gabriela Petruşel Let $$(X, \left\langle \cdot \right\rangle )$$ be a Hilbert space and $$T:X\rightarrow X$$ be a decreasing operator. Under a metric condition involving the convex combination of x and T(x), we will prove some fixed point theorems which generalize and complement several results in the theory of nonlinear operators. Our results are closely related to the admissible perturbations approach in fixed point • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-05-20 Huabo Zhang In this paper, we are interested in the existence of ground state nodal solutions for the following Schrödinger–Kirchhoff-type Laplacian problems:$$\begin{aligned} -M\bigg (\int _{{\mathbb {R}}^{3}}|\nabla u|^{2}\mathrm{{d}}x\bigg )\Delta u+V(x)u=|u|^{4}u+ k f(u),\;x\in {\mathbb {R}}^{3}, \end{aligned}$$where $$M(t)=a+bt^\gamma$$ with $$0<\gamma <2$$, $$a,b>0$$ and the nonlinear function $$f\in • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-05-10 Krzysztof Ciepliński Using the fixed point method, we prove the Ulam stability of two general functional equations in several variables in 2-Banach spaces. As corollaries from our main results, some outcomes on the stability of a few known equations being special cases of the considered ones will be presented. In particular, we extend several recent results on the Ulam stability of functional equations in 2-Banach spaces • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-04-29 S. Sadiq Basha A new class of cyclic mappings, known as almost cyclic contractions, is introduced. Indeed, it is interesting to see that almost cyclic contractions are weaker than cyclic contractions. The main purpose of this article is to explore the existence of a best approximation but not a best proximity point for almost cyclic contractions. Further, it is interesting to observe that a best proximity point theorem • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-04-20 Dirk Hennig The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein–Gordon systems with convex on-site potentials is proved. The existence problem of localised solutions is expressed in terms of a fixed point equation for an operator on some appropriate function space which is solved by means of Schauder’s Fixed Point Theorem. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-04-19 Mohsen Masoudi, Abbas Salemi In this paper, the Hermitian positive definite solutions of the matrix equation \(X^s +A^* X^{ - t}A = Q$$, where A is an $$n \times n$$ nonsingular complex matrix, Q is an $$n \times n$$ Hermitian positive definite matrix and $$s, t> 0$$, are discussed. Some conditions for the existence of Hermitian positive definite solutions of this equation are derived. In addition, two iterative methods to obtaining • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-04-15 Christopher S. Goodrich We consider both Hammerstein integral equations and nonlocal boundary value problems in possession of two different nonlocal elements. The first occurs in the differential equation itself and takes the form $$\Vert u\Vert _q^q$$. The second occurs in the boundary condition and takes the form of a Stieltjes integral. Because the nonlocal elements are not necessarily related, a careful analysis is required • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-04-13 Nihal Özgür, Nihal Taş Recently, the discontinuity problem at a fixed point has been studied by various aspects. In this paper, we investigate new solutions to the discontinuity problem using appropriate contractive conditions which are strong enough to generate fixed points (resp. common fixed points) but which do not force the map (resp. maps) to be continuous at fixed points. An application is also given to the fixed-circle • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-04-10 J. Caballero, B. López, K. Sadarangani In this paper, we study the existence of positive solutions for the following nonlinear fractional boundary value problem:$$\begin{aligned} \left. \begin{array}{ll}D^{\alpha }_{0^+} u(t)+f(t,u(t),(Hu)(t))=0,&{} 0

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-25
Maher Berzig, Imed Kedim

In this paper, we introduce the concept of Eilenberg–Jachymski collection on a nonempty set. Then, we establish three results equivalent to Bourbaki–Kneser’s fixed point theorem, and, therefore, to the axiom of choice. As consequences, we present new fixed point theorems in compact topological spaces, which extend and unify those of Nemytskii–Edelstein, Liepinš and Suzuki.

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-20
Ming Zhu, Rong Hu, Ya-Ping Fang

The Douglas–Rachford splitting method is a classical and powerful method that is widely used in engineering fields for finding a zero of the sum of two operators. In this paper, we begin by proposing an abstract second-order dynamic system involving a generalized cocoercive operator to find a zero of the operator in a real Hilbert space. Then we develop a second-order adaptive Douglas–Rachford dynamic

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-17
Jean-Paul Brasselet, Tatsuo Suwa

For two differentiable maps between two manifolds of possibly different dimensions, the local and global coincidence homology classes are introduced and studied by Bisi-Bracci-Izawa-Suwa (2016) in the framework of Čech-de Rham cohomology. We take up the problem from the combinatorial viewpoint and give some finer results, in particular for the local classes. As to the global class, we clarify the relation

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-16

In this paper, we prove some common fixed point theorems for one-parameter semigroups of asymptotically regular mappings which satisfy certain generalized Lipschitzian conditions in metric spaces. Our results do not assume the continuity of the mappings in the semigroups. The results extend some relevant common fixed point theorems in Górnicki (Colloq Math 64:55–57, 1993), Imdad and Soliman (Fixed

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-16
Duong Thi Kim Huyen, Jen-Chih Yao

The concept of minimax variational inequality was proposed by Huy and Yen (Acta Math Vietnam 36, 265–281, 2011). This paper establishes some properties of monotone affine minimax variational inequalities and gives sufficient conditions for their solution stability. Then, by transforming a two-person zero sum game in matrix form (Barron in Game Theory. An Introduction, 2nd edn, Wiley, New Jersey, 2013)

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-15
Yun Xin, Zhibo Cheng

In this paper, we investigate the existence of a positive periodic solution for the following $$\phi$$-Laplacian generalized Liénard equation with a singularity: \begin{aligned} (\phi (u'))'+f(t,u)u'+ \frac{b(t)}{u^\rho }=h(t)u^m, \end{aligned} where $$\rho$$ is a positive constant and m is a constant. Our proof is based on the Manásevich–Mawhin continuation theorem, and the results are applicable

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-10
Kanokwan Sawangsup, Wutiphol Sintunavarat

The aim of this work is to introduce the concept of an $$(F,\gamma )_{\mathfrak {R}}$$-contraction which is a weak idea of an F-contraction in metric spaces endowed with a binary relation. Fixed point results for such new contractions are investigated, and its benefit is showing from an example. As applications, we apply theoretical results together with the Thompson metric for solving nonlinear matrix

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-08
José Carlos de Albuquerque, Gelson G. dos Santos, Giovany M. Figueiredo

In this paper we are concerned with existence and behavior of positive solutions to the following class of linearly coupled elliptic systems with discontinuous nonlinearities \begin{aligned} \left\{ \begin{array}{ll} -\Delta u+V_{1}(x)u = H(u-\beta )f_{1}(u)+ a(x)v, &{} \text {in } {\mathbb {R}}^{N},\\ -\Delta v+V_{2}(x)v = H(v-\beta )f_{2}(v)+ a(x)u, &{} \text {in } {\mathbb {R}}^{N},\\ u,v\in D^{1 • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-01 Marcio Colombo Fenille We study the coincidence problem (i.e., the possibility of annihilating the coincidences of a pair of maps by way of homotopy deformations) for pairs of maps from a closed surface into a graph. We consider maps which may be decomposed as two auxiliary maps, according to a decomposition of the surface as a connected sum. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-03-01 Ahmed Nuino Using the Brzḑek’s fixed point approach, we will prove the generalized Hyers–Ulam–Rassias stability for the following Drygas functional equation in 2-Banach spaces\begin{aligned} f(x+y)+f(x-y)=2f(x)+f(y)+f(-y). \end{aligned}$$Moreover, we investigate some hyperstability results for this equation. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-02-27 Simeon Reich, Truong Minh Tuyen To solve the split common null point problem with multiple output sets in Hilbert spaces, we introduce two new self-adaptive algorithms and prove strong convergence theorems for both of them. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-02-24 Mihály Bessenyei, Zsolt Páles The renorming technique allows one to apply the Banach Contraction Principle for maps which are not contractions with respect to the original metric. This method was invented by Bielecki and manifested in an extremely elegant proof of the Global Existence and Uniqueness Theorem for ODEs. The present paper provides further extensions and applications of Bielecki’s method to problems stemming from functional • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-02-24 Sumit Chandok, R. K. Sharma, Stojan Radenović In this manuscript, we give a partial answer to Reich’s problem on multivalued contraction mappings and generalize Mizoguchi–Takahashi’s fixed point theorem using a new approach of multivalued orthogonal $$(\tau ,F)$$-contraction mappings in the framework of orthogonal metric spaces. We give a nontrivial example to prove the validity of our results. Some interesting consequences are also deduced. Finally • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-02-18 Amira Makhlouf, Dalila Azzam-Laouir, Charles Castaing In this paper, we consider evolution problems involving time-dependent maximal monotone operators in Hilbert spaces. Existence and relaxation theorems are proved. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-02-17 Mohamed Khazou, Mohamed Aziz Taoudi In this paper, we employ partial order method, cone theory, and the techniques of measure of weak noncompactness to prove several new theorems on the existence and the uniqueness of fixed points or coupled fixed points for operators satisfying some monotonicity assumptions. Our conclusions generalize and improve several well-known results. As an application, we investigate the existence of a unique • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-01-28 Bin-Sheng Wang, Gang-Ling Hou, Bin Ge The double-phase problem with a reaction term depending on the gradient is considered in this paper. Using the topological degree theory for a class of demicontinuous operators, we prove the existence of at least one solution of such problem. Our assumptions are suitable and different from those studied previously. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-01-10 Ruyun Ma, Zhiqian He In this paper, we are considered with the Dirichlet problem of quasilinear differential system, involving the mean curvature operator in Minkowski space$$\begin{aligned} {\mathcal {M}}(w)=\text {div}\left( \frac{\nabla w}{\sqrt{1-|\nabla w|^2}}\right) , \end{aligned}$$in a ball in $${\mathbb {R}}^N$$. Using global bifurcation technique, we obtain the existence of an unbounded branch of positive radial • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-01-10 Lizhen Qin In a previous paper, under the assumption that the Riemannian metric is special, the author proved some results about the moduli spaces and CW structures arising from Morse theory. By virtue of topological equivalence, this paper extends those results by dropping the assumption on the metric. In particular, we give a strong solution to the following classical question: Does a Morse function on a compact • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-01-08 Afrah A. N. Abdou, M. A. Khamsi In this paper, we reexamine the concept of firmly nonexpansiveness in the modular sense in the variable exponent sequence spaces $$\ell _{p(\cdot )}$$. In particular, we extend the classical fixed point results for firmly nonexpansive mappings defined in Banach spaces to the modular case within the spaces $$\ell _{p(\cdot )}$$. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-01-01 Ruyun Ma, Dongliang Yan In this paper, we study the global bifurcation of positive radial solutions for some semilinear elliptic problems of order 2m in an annulus with Dirichlet boundary conditions. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2021-01-01 Shane Kepley, Tianhao Zhang We give a constructive proof of the classical Cauchy–Kovalevskaya theorem for ordinary differential equations which provides a sufficient condition for an initial value problem to have a unique, analytic solution. Our proof is inspired by a modern numerical technique for rigorously solving nonlinear problems known as the radii polynomial approach. The main idea is to recast the existence and uniqueness • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-11-26 Shih-sen Chang, L. Wang, L. C. Zhao, X. D. Liu The purpose of this article is twofold. One is to establish a proximal point algorithm for finding a minimizer of a proper convex and lower semi-continuous function and fixed points of quasi-pseudo-contractive mappings in CAT(0) spaces. The other is to point out and correct a basic and conceptual error in a paper of Ugwunnadi et al. [Theorem 3.1, J. Fixed Point Theory Appl. (2018) 20: 82]. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-11-21 Victor Zvyagin, Mikhail Turbin In the present paper, we study weak solvability of the optimal feedback control problem for the inhomogeneous Voigt fluid motion model. The proof is based on the approximation-topological approach. This approach involves the approximation of the original problem by regularized operator inclusion with the consequent application of topological degree theory. Then, we show the convergence of the sequence • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-11-17 A. Dukov, Yu. Ilyashenko Bifurcations that occur in a small neighborhood of a polycycle of a planar vector field are called semilocal. We prove that even semilocal bifurcations of hyperbolic polycycles may have numeric invariants of topological classification. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-11-13 Xinqiu Zhang, Lishan Liu, Yonghong Wu In this paper, we present a new fixed point theorem for the sum of two mixed monotone operators of Meir–Keeler type on ordered Banach spaces through projective metric, which extends the existing corresponding results. As applications, we utilize the results obtained in this paper to study the existence and uniqueness of positive solutions for nonlinear singular fourth-order elastic beam equations with • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-11-13 Farhang Jahangir, Pouya Haghmaram, Kourosh Nourouzi A new generalization of the metric space notion, named $${\mathcal {F}}$$-metric space, was given in [M. Jleli, B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl. 20 (2018), no. 3, Art. 128, 20 pp.]. In this paper, we investigate some properties of $${\mathcal {F}}$$-metric spaces. A simple proof is given to show that the natural topology induced by an $${\mathcal {F}}$$-metric • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-11-01 Abdelkader Dehici, Najeh Redjel In this paper, we give an investigation of the asymptotics for the iterations associated with (c)-mappings acting on unbounded closed convex subsets of Banach spaces. In particular, the almost fixed point property (in short; AFPP) and conditions ensuring an ergodic type theorem for this class of mappings are established. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-29 C. Izuchukwu, A. A. Mebawondu, O. T. Mewomo In solving the split variational inequality problems in real Hilbert spaces, the co-coercive assumption of the underlying operators is usually required and this may limit its usefulness in many applications. To have these operators freed from the usual and restrictive co-coercive assumption, we propose a method for solving the split variational inequality problem in two real Hilbert spaces without • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-19 Cristian Chifu, Adrian Petruşel, Gabriela Petruşel In this paper, we will present some fixed point results for the case of non-self operators satisfying a nonlinear graphic contraction condition in complete metric spaces. Properties of the corresponding fixed point equation are established and some applications are given. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-14 Ning Lu, Fei He, Shufang Li In this work, a counterexample is given to refute a result in the paper by Younis et al. (J Fixed Point Theory Appl 21:1–33, 2019). Furthermore, applying this counterexample, we give negative answers to some of the open problems in their paper. Recently, Baradol et al. give a new theorem to rectify the result of Younis et al. However, we find that there are some gaps in the proofs of their results • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-10 Donghoon Jang In this paper, we prove that if the circle acts on an 8-dimensional compact almost complex manifold M with 4 fixed points, all the Chern numbers and the Hirzebruch $$\chi _y$$-genus of M agree with those of $$S^2 \times S^6$$. In particular, M is unitary cobordant to $$S^2 \times S^6$$. • J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-06 Bianca Satco, George Smyrlis We are concerned with the study of a first-order nonlinear periodic boundary value problem$$\begin{aligned} \left\{ \begin{array}{l} u'_g(t)+b(t) u(t) =f(t,u(t)),\; t\in [0,T]\\ u(0)=u(T) \end{array} \right. \end{aligned}(1) involving the Stieltjes derivative with respect to a left-continuous nondecreasing function. Based on Schaeffer’s fixed point theorem and making use of a notion of partial Stieltjes

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-04
Torrey M. Gallagher, Maria Japón, Chris Lennard

Let C be a convex subset of a Banach space X and let T be a mapping from C into C. Fix $$\alpha =(\alpha _1,\alpha _2,\ldots ,\alpha _n)$$ a multi-index in $${\mathbb {R}}^n$$ such that $$\alpha _i\ge 0$$ ($$1\le i\le n$$), $$\sum _{i=1}^n\alpha _i=1$$, $$\alpha _1,\alpha _n>0$$, and consider the mapping $$T_\alpha :C\rightarrow C$$ given by $$T_\alpha =\sum _{i=1}^n \alpha _i T^i$$. Every fixed point

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-04
Afif Ben Amar, Saoussen Derbel, Donal O’Regan

The purpose of this paper is to prove fixed point results for certain types of countably asymptotically $$\Phi$$-nonexpansive (or countably $$\Phi$$-condensing) operators on locally convex spaces and satisfying additional asymptotic contractive-type conditions. These results allow us to obtain generalizations of recent fixed point theorems of Ben Amar, Isac, Németh, O’Regan, and Touati to locally

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-02
Zdzisław Dzedzej, Tomasz Gzella

The notion of homotopy in the category of morphisms introduced by Górniewicz and Granas is proved to be equivalence relation which was not clear for years. Some simple properties are proved and a coincidence point index is described.

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-02
Bancha Panyanak

Using the viscosity approximation method introduced by Moudafi (J Math Anal Appl 241:46–55, 2000), we can obtain strong convergence theorems for monotone increasing G-nonexpansive mappings in Hadamard spaces endowed with graphs. We also give sufficient conditions for the existence of solutions of the variational inequality problem in this setting. Our results generalize and improve many results in

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-10-01
Rubén Figueroa, Rodrigo López Pouso, Jorge Rodríguez–López

We obtain a new fixed point index theory for a class of not necessarily continuous operators in cones. We employ this tool to prove a discontinuous version of Leggett–Williams’ fixed point theorem. Finally, we establish new existence and multiplicity criteria for a second-order three point BVP with discontinuous nonlinearities.

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-09-30
Lili Chen, Ni Yang, Yanfeng Zhao, Zhenhua Ma

In this paper, we first introduce the concept of graphical convex metric spaces and some basic properties of the underlying spaces. Different from related literature, we generalize Mann iterative scheme and Agrawal iterative scheme for set-valued mappings to above spaces by introducing the concepts of T-Mann sequences and T-Agrawal sequences. Furthermore, by using the iterative techniques and graph

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-09-26
Behnam Matani, Jamal Rezaei Roshan

In this work, we introduce the concepts of multivariate generalized Meir–Keeler condensing operator, and multivariate L-function and prove some new fixed point theorems with the aid of the measure of non-compactness. Our results generalize and extend a lot of comparable results in the literature. Also, we use these results to discuss the solvability for a system of functional integral equations of

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-09-22
Djamila Derouiche, Hichem Ramoul

The purpose of this paper is to introduce the notions of extended F-contraction of Hardy–Rogers type, extended F-contraction of Suzuki–Hardy–Rogers type and generalized F-weak contraction of Hardy–Rogers type and to establish some new fixed point results for such kind of mappings in the setting of complete b-metric spaces. These fixed point results improve (and/or) extend those obtained in Vetro (Nonlinear

• J. Fixed Point Theory Appl. (IF 2.11) Pub Date : 2020-09-14