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In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, by considering theWardowski's technique, we present fixed point results for multivalued mapping on a space with two metrics. Also, taking into account β-admissibility of a multivalued mapping, we provide some more general results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper, we establish the generalized viscosity implicit rules of asymptotically nonexpansive mappings in CAT(0) spaces. The strong convergence theorems of the implicit rules proposed are proved under certain assumptions imposed on the control parameters. The results presented in this paper improve and extend some recent corresponding results announced. [ABSTRACT FROM AUTHOR]

In this paper we define-admissibility of multi-valued mapping with respect to a single-valued mapping and use this concept to establish a coincidence point theorem for pairs of nonlinear multi-valued and single-valued mappings under the assumption of an inequality with rational terms. We illustrate the result with an example. In the second part of the paper we prove the stability of the coincidence point sets associated with the pairs of mappings in our coincidence point theorem. For that purpose we define the corresponding stability concepts of coincidence points. The results are primarily in the domain of nonlinear set-valued analysis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new extragradient method with regularization for finding a common element of the solution set Γ of the split feasibility problem and the set Fix(S) of fixed points of a nonexpansive mapping S in infinitedimensional Hilbert spaces, combining the regularization method and the technique of averaged operator, we prove the sequences generated by the proposed algorithm converge weakly to an element of Fix(S)∩Γ under mild conditions. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper, we discuss the convergence theorems for the double acting iterative scheme to a common fixed point for a family of generalized φ-weak contraction mappings in CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce several types of Meir-Keeler contractive mappings in the structure of Ms-metric spaces. Then we study some existence and uniqueness fixed point theorems for these types of MKC mappings in Ms-metric spaces via Gupta-Saxena type contraction and other fraction version type contractions. Also, we extend and improve very recent results in fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a proximal point iterative algorithm with general errors for monotone mappings in Banach spaces. We prove that the proposed algorithm converges strongly to a proximal point for monotone mappings. Our theorems in this paper improve and unify most of the results that have been proposed for this important class of nonlinear mappings. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of C-class fuction, we prove the existence of common fixed point for generalized Zam rescu-type mappings and generalized weakly Zam rescu-type mappings. Our results generalize so many results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we discuss some topological properties of the set F(S0, T,z):= {x ∊ X : S0 x ∊ Tx + zg, where T is a nonlinear multi-valued mappings and S0 is a single-valued mappings acting on a Banach space X. This study is based on a new concept, the so called weakly relative demicompactness for nonlinear operators. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new fixed point theorems for a 2×2 block operator matrix defined on nonempty, bounded, closed, and convex subsets of Banach algebras, where the inputs are multi-valued mappings. The obtained results are then applied to a coupled system of perturbed functional differential inclusions of initial and boundary value problems in order to prove the existence of solutions under a Carathéodory condition. [ABSTRACT FROM AUTHOR]

The main results of the paper concern the existence of fixed points of nonlinear F-contraction and the sum of this type of mapping with a compact operator. The results of Krasnosel’skii type are obtained with a usage of the Hausdorff measure of noncompactness and condensing mappings. The presented new tools give the possibility to verify the existence problems of the solutions for some classes of integral equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find out fixed point results for semi-α⁎-dominated multivalued mappings fulfilling a new generalized locally F-dominated multivalued contractive condition on a closed ball in complete dislocated metric space. Example and application both are given to show the novelty of our results. Our results merge, extend, and infer many results. [ABSTRACT FROM AUTHOR]

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536-545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems in G-metric spaces for contraction mappings. Our results generalize some well known results in literature. [ABSTRACT FROM AUTHOR]

Meir and Keeler formulated their fixed point theorem for contractive mappings with purely metric condition. This idea was extended by numerous mathematicians. In this paper, we present a simple method of proving such theorems and give new results. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to present three classes of cyclic (α, β)-(ψ, θ, φ)-admissible multivalued mappings, and then prove the existence of fixed point in a complete metric space. Our results generalize and extend several works. Two examples were added to support our work. [ABSTRACT FROM AUTHOR]

Existence of fixed point for C-class functions was first proved by Ansari in 2014. Then, many authors gave interesting results using C-class functions. In this paper, we prove the existence of strong coupled proximity point for generalised cyclic coupled proximal maps. Our result generalises the results of Kadwin and Marudai. [ABSTRACT FROM AUTHOR]

In this paper, we establish a convergence theorem for fixed points of generalised weak contractions in complete metric spaces under some new control conditions on the functions. An illustrative example of a generalised weak contraction is discussed to show how the new conditions extend known results. [ABSTRACT FROM PUBLISHER]

This paper is concerned with a host-macroparasite difference model. By applying the contraction mapping fixed point theorem, we prove the existence of unique almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Lyapunov functional. [ABSTRACT FROM AUTHOR]

Let $(X,\|\cdot\|)$ be a Banach space. Let C be a nonempty, bounded, closed, and convex subset of X and $T: C \rightarrow C$ be a monotone nonexpansive mapping. In this paper, it is shown that a technique of Mann which is defined by is fruitful in finding a fixed point of monotone nonexpansive mappings. [ABSTRACT FROM AUTHOR]

In this paper, several kinds of generalized vector quasi-equilibrium problems are introduced and studied in abstract convex spaces. Using the properties of Γ-convex and $\mathfrak{KC}$-maps, some sufficient conditions are given to guarantee the existence of solutions in connection with these generalized vector quasi-equilibrium problems. As applications, some existence theorems of solutions for the generalized semi-infinite programs with vector quasi-equilibrium constraints are also given. [ABSTRACT FROM AUTHOR]

In the paper, we introduce a new hybrid algorithm which is not based on the modification to weak convergence algorithms. The strong convergence theorem of the proposed algorithm is presented. Finally, the numerical experiments suggest that the new algorithm could be faster than Nakajo and Takahashi's algorithm in J. Math. Anal. Appl. 279:372-379, 2003. [ABSTRACT FROM AUTHOR]

In this paper, a new modified Ishikawa iterative algorithm with errors by a shrinking projection method for generalized mixed equilibrium problems and a countable family of uniformly Bregman totally quasi- D-asymptotically nonexpansive mappings is introduced and investigated in the framework of a real Banach space. Strong convergence of the sequence generated by the proposed algorithm is derived under some suitable assumptions. These results are new and develop some recent results in this field. [ABSTRACT FROM AUTHOR]

In this paper, we prove some strong and △-convergence theorems for a finite family of multivalued quasi-nonexpansive mappings satisfying condition $(E)$ in $\operatorname{CAT}(\kappa)$ spaces. Our results extend the corresponding results of Abkar and Eslamian (Nonlinear Anal. 75:1895-1903, 2012), Panyanak (Fixed Point Theory Appl. 2014:1, 2014), Shahzad and Zegeye (Nonlinear Anal. 71:838-844, 2009) and many others. [ABSTRACT FROM AUTHOR]

Recently, Cui and Wang (2014) constructed an algorithm for demicontractive operators that converges weakly, under mild assumptions, to some solution of the split common fixed point problem. In this paper, based on Halpern’s type method (1967), we construct an algorithm for demicontractive operators that produces sequences that always converge strongly to a specific solution of the split common fixed point problem. Particular cases of directed operators and quasi-nonexpansive mappings are also considered. [ABSTRACT FROM AUTHOR]

In this paper, we prove common fixed point theorems for two mappings under the condition of R-weakly commuting in complete S-metric spaces. A lot of fixed point theorems on ordinary metric spaces are special cases of our main result. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the concepts of weakly biased mappings and occasionally weakly biased mappings for a pair of self-mappings in Menger PM-spaces, some new common fixed point theorems under contractive conditions are obtained. Some examples are also given to exemplify our main results. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce the notion of weakly upper semicontinuous set-valued maps and to establish a new fixed-point theorem. The set-valued maps with an approximating upper semicontinuous selection property are also defined. Next, we use our fixed-point result to obtain equilibrium existence in abstract economies with two constraints, which provide a natural scenario for potential applications of our approach to general equilibrium theory. In this regard, we set models of economies with asymmetric informed agents, who are able to improve their initial information through market signals. These economies offer examples in which the informational feasibility requirement represents an additional constraint. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of integral equations and apply the coincidence and common fixed point theorems for four mappings satisfying a (ψ, α, β)-weakly contractive condition in ordered metric spaces to prove the existence of a common solution to integral equations. Also we furnish suitable examples to demonstrate the validity of the hypotheses of our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider two families Ψ1 and Ψ2 of mappings defined on [0,+∞) satisfy some certain properties. Using the mentioned properties for Ψ1 and Ψ2, we prove the analogous PPF dependent fixed point theorems for mappings as in Drici et al. (Nonlinear Anal. 67:641-647, 2007) in partially ordered Banach spaces where mappings satisfy the weaker contractive conditions without assuming the topological closedness with respect to the norm topology for the Razumikhin class Rc. [ABSTRACT FROM AUTHOR]

We recall the concepts of {α, ξ}-contractive and α-admissible mappings on complete metric spaces to state related fixed point theorems. In this paper, we obtain some fixed point results for {α, ξ}-expansive locally contractive mappings in complete metric spaces. The contractiveness of the mapping is only on a closed ball instead of the whole space. Our results unify, generalize, and complement various well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish certain new fixed point results for multi-valued as well as single-valued maps satisfying an α-ψ-contractive conditions in complete metric space. As an application, we derive some new fixed point theorems for ψ-graphic contractions defined on a metric space endowed with a graph as well as an ordered metric space. The presented results complement and extend some very recent results proved by Asl et al. (Fixed Point Theory Appl. 2012:212, 2012) and Samet et al. (Nonlinear Anal. 75:2154-2165, 2012) as well as other theorems given by Hussain et al. (Fixed Point Theory Appl. 2013:212, 2013). Some comparative examples are constructed which illustrate the superiority of our results to the existing ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we utilize the notion of common limit range property with variants of R-weakly commuting mappings and obtain some common fixed point theorems in intuitionistic fuzzy metric spaces. We give some illustrative examples which support our results. Consequently a host of common fixed theorems are generalized and improved [ABSTRACT FROM AUTHOR]

In this paper, we give examples of cyclic operators defined on various types of sets, in order to illustrate some results in the extremely rich literature following the seminal paper [Kirk,W. A., Srinivasan, P. S. and Veeramani, P., Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), No. 1, 79 - 89]. All examples which are presented enrich the list of cyclic operators and give a subject to future studies of this type of operators. [ABSTRACT FROM AUTHOR]

In this paper, we study a zero point problem of the sum of two accretive operators based on a viscosity forward-backward iterative algorithm with computational errors. Strong convergence results are established in the framework of q-uniformly smooth Banach spaces. We also apply the strong convergence results to solve variational inequality problems, convex minimization problems and fixed point problems. [ABSTRACT FROM AUTHOR]

Most of the studies about hybrid mappings are carried out for single-valued mappings in Hilbert spaces. We define a new class of multivalued mappings in CAT (κ) spaces which contains the multivalued generalization of (α, β) - hybrid mappings defined on Hilbert spaces. In this paper, we prove existence and convergence results for a new class of multivalued hybrid mappings on CAT(κ) spaces which are more general than Hilbert spaces and CAT(0) spaces. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iterative process involving a hybrid pair of a Bregman strongly nonexpansive single-valued mapping and a finite family of Bregman relative nonexpansive multi-valued mappings and prove strong convergence theorems of the proposed iterative process in reflexive Banach spaces under appropriate conditions. Our main results can be viewed as an improvement and extension of the several results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a monotone (α, β)-nonexpansive mapping in an ordered Banach space E with the partial order ≤ and prove some existence theorems of fixed points of a monotone (α, β)-nonexpansive mapping in a uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of Ishikawa type iteration under the control condition ... Finally, we give an numerical example to illustrate the main result in this paper. [ABSTRACT FROM AUTHOR]

The question of continuity of contractive map and in particular continuity at fixed points emerged with the publication of research papers by R. Kannan in 1968 and 1969 respectively. In fact continuity of a map is essential prerequisite for establishing fixed point. Probably the foremost common fixed point theorem without using the notion of continuity was established by Pant [Discontinuity and fixed points, J. Math. Anal. Appl., 240(1999), 284-289] when he introduced the idea of non-compatibility. First weaker form of continuity known as reciprocal continuity was also introduced by Pant [A common fixed point theorem under a new condition, Indian J. Pure Appl. Math., 30(1999), No. 2, 147-155]. Subsequently several generalizations of this notion have been obtained. Our aim is to discuss brief development of weaker forms of continuity of maps in fixed point consideration. Further coincidence and common fixed point for noncommuting discontinuous maps via Meir-Keeler contractions on non complete MC-space without using containment of range space of involved maps are obtained and illustrated by examples. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point theorems which are variants of Achari and Ćirić-Jotić types for mappings having non-unique fixed points by employing some hybrid contractive conditions. Our results generalize, extend and improve some previous and corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

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 proved are improvement of the results of Censor et al. (J. Optim. Theory Appl. 148:318-335, 2011). [ABSTRACT FROM AUTHOR]

In this paper, we study a modified S-iteration process involving two asymptotically quasi-nonexpansive mappings. We prove that the sequence generated by this process converges to a common fixed point of the above mentioned mappings. A sufficient condition for convergence to common fixed points has also been given. Our results extend and improve many known results from the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of operators, for which a fixed point theorem is proven. This class of mappings is very large and unifies several classes of contractive type operators from the literature, including Berinde mappings. Such fact is proven via a comparison with various metrical contractive type mappings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to state some generalizations of the main results in [M.A. Ahmed: A common fixed point theorem for expansive mappings in 2-metric spaces and its application, Chaos Solitons Fract., 42(2009), 2914-2920]. Examples are given to illustrate the results. [ABSTRACT FROM AUTHOR]