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We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

The first purpose of this paper is to prove an existence and uniqueness result for the multivariate fixed point of a contraction type mapping in complete metric spaces. The proof is based on the new idea of introducing a convenient metric space and an appropriate mapping. This method leads to the changing of the non-self-mapping setting to the self-mapping one. Then the main result of the paper will be applied to an initial-value problem related to a class of differential equations of first order. The second aim of this paper is to prove strong and weak convergence theorems for the multivariate fixed point of a N-variables nonexpansive mapping. The results of this paper improve several important works published recently in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the concept of cone 2-metric spaces over Banach algebras is introduced and some existence and uniqueness theorems of fixed points for some mappings satisfying certain contractive conditions are established. As an application of one of the main results, an example is given at the end of the paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study stability and strong convergence of asymptotically pseudocontractive mappings by using a new composite implicit iteration process in an arbitrary real Banach space. The results in this paper improve and extend the corresponding results in the literature. [ABSTRACT FROM AUTHOR]

In this paper the fixed point of multivalued mapping is considered. A generalization of the well-known Nadler contraction principle, the Khan contraction theorem and the fixed point theorem in complete metric space with a convex structure is proved. The main result of the paper is formulated by three theorems where the mappings, defined over the complete metric space, are assumed to satisfy some integral type of contraction. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a new class of probabilistic normed spaces and to study fixed point problems in this class of probabilistic normed spaces. This paper includes the following two contents: (1) The definition of a new class of probabilistic normed spaces, the so-called S-probabilistic normed spaces, is given. In order to study the fixed point problems, some relevant properties of S-probabilistic normed spaces are discussed and some basic useful results are obtained; (2) The notion of probabilistic weak convergence is firstly presented in this paper. Therefore the probabilistic weak and strong convergence theorems of fixed points for nonexpansive mappings, asymptotically nonexpansive mappings and strongly pseudocontractive mappings are also proved by using the new methods and techniques. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and consider a new hybrid shrinking projection algorithm for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of a system of variational inequality problems, the set of solutions of a system of optimization problems, the common fixed point set of a uniformly closed family of countable quasi-Bregman strictly pseudocontractive mappings in reflexive Banach spaces. Strong convergence theorems have been proved under the appropriate conditions. The main innovative points in this paper are as follows: (1) the notion of the uniformly closed family of countable quasi-Bregman strictly pseudocontractive mappings is presented and the useful conclusions are given; (2) the relative examples of the uniformly closed family of countable quasi-Bregman strictly pseudocontractive mappings are given in classical Banach spaces $l^{2}$ and $L^{2}$; (3) the hybrid shrinking projection method presented in this paper modified some mistakes in the recent result of Ugwunnadi et al. (Fixed Point Theory Appl. 2014:231, 2014). These new results improve and extend the previously known ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study viscosity approximations with $(\psi,\varphi)$ -weakly contractive mappings. We show that Moudafi's viscosity approximations follow from Browder and Halpern type convergence theorems. Our results generalize a number of convergence theorems including a strong convergence theorem of Song and Liu (Fixed Point Theory Appl. 2009:824374, 2009). [ABSTRACT FROM AUTHOR]

In this paper, we obtain some best proximity point results for a new class of non-self mappings T : A ⟶ B called special generalized proximal β-quasi contractive. Our result is illustrated by an example. Several consequences are derived. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of generalized nonexpansive mappings. Some new fixed point theorems for these mappings are obtained. [ABSTRACT FROM AUTHOR]

In this paper we utilize a generalized weakly contractive mapping to establish some best proximity point results which are global optimization results for finding the minimum distances between two sets. Amongst many approaches to this problem, we adopt the approach where the problem is treated as that of finding global optimal approximate solution of the fixed point equation for the generalized weak contraction mapping. We use three control functions to define such mappings. The results are obtained in metric spaces with a partial ordering defined therein. There is a blending of analytic and order theoretic approaches in the proofs. The uniqueness is obtained by imposing some order theoretic conditions additionally. There are several corollaries. An illustration of the main theorem through an example is given which also shows that the corollaries are properly contained in the main theorem. [ABSTRACT FROM AUTHOR]

The paper concerns our sustained efforts for introduction of V-fuzzy metric spaces and to study their basic topological properties. As an application of this concept, we prove coupled common fixed point theorems for mixed weakly monotone maps in partially ordered V-fuzzy metric spaces. An example quoted in this paper also corroborates fully the main result. Also, here we introduce the concept of a symmetric V-fuzzy metric space. Under the influence of symmetry property of V-fuzzy metric spaces, its conversion materializes to the main result from V-fuzzy metric spaces to fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, first, we introduce the condition (BP) which is weaker than the completely continuous mapping in Banach spaces. Second, we consider a simple iteration and prove some strong convergence theorems of the proposed iteration for an asymptotically nonexpansive nonself-mapping with the condition (BP). Finally, we give two examples to illustrate the main result in this paper. Our results improve and extend the corresponding results given by some authors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the extra-gradient methods for solving split feasibility and fixed point problems involved in pseudo-contractive mappings in real Hilbert spaces. We propose an Ishikawa-type extra-gradient iterative algorithm for finding a solution of the split feasibility and fixed point problems involved in pseudo-contractive mappings with Lipschitz assumption. Moreover, we also suggest a Mann-type extra-gradient iterative algorithm for finding a solution of the split feasibility and fixed point problems involved in pseudo-contractive mappings without Lipschitz assumption. It is proven that under suitable conditions, the sequences generated by the proposed iterative algorithms converge weakly to a solution of the split feasibility and fixed point problems. The results presented in this paper extend and improve some corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a new general hybrid iterative algorithm for finding a common element of the set of common zeros of two families of finite maximal monotone mappings, the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space. Our algorithm is based on four well-known methods: Mann's iteration method, composite method, outer-approximation method and extragradient method. We prove the strong convergence theorem for the proposed algorithm. The results presented in this paper extend and improve the corresponding results of Wei and Tan (Fixed Point Theory Appl. 2014:77, 2014). Some special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for solving split equality mixed equilibrium problems in the framework of infinite-dimensional real Hilbert spaces. The strong and weak convergence theorems are obtained. As application, we shall utilize our results to study the split equality mixed variational inequality problem and the split equality convex minimization problem. Our results presented in this paper improve and extend some recent corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the setting of multiplicative metric spaces to establish results regarding the common fixed points of four mappings, using a contraction condition defined by means of a comparison function. Also, we provide illustrative examples in support of our new results. The results obtained in this paper extend and improve some well-known comparable results in the literature due to He et al. (Fixed Point Theory and Appl. 2013:48, 2013). [ABSTRACT FROM AUTHOR]

In this paper, the concept of ordered contractive mappings is introduced on cone metric spaces over Banach algebras, and some existence theorems of fixed points for such mappings are obtained. As an application of a result, an example is given at the end of the paper. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove a more generalized contraction mapping principle. By using this more generalized contraction mapping principle, a further generalized best proximity theorem was established. Some concrete results have been derived by using the above two theorems. The results of this paper improve many important results published recently in the literature. [ABSTRACT FROM AUTHOR]

In this work, we introduce the $(\mathit{CLR})$-property for the hybrid pairs of single-valued and multi-valued mappings and give some coincidence and common fixed point theorems for the hybrid pairs of some contractive conditions. Also, we will give some examples to illustrate the main results in this paper. Our results extend and improve some results given by some authors. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $(\alpha,\theta,k)$-contraction multi-valued mappings and establish some fixed point results for such mappings by using some control functions due to Jleli et al. (J. Inequal. Appl. 2014:439, 2014) in metric spaces and furnish some interesting examples to illustrate our main results. Also, we give some fixed point results in metric spaces endowed with a graph. Our results generalize and extend recent results given by some authors. [ABSTRACT FROM AUTHOR]

After the appearance of Nieto and Rodríguez-López's theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function α, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of $(\alpha,\psi)$-rational type contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed point for such class of generalized nonlinear contractive mappings in the setting of generalized metric spaces. We also deduce several interesting corollaries. [ABSTRACT FROM AUTHOR]

We study self-mappings on complete metric spaces, which we refer to as higher-order Lipschitz mappings. These mappings generalise Lipschitz mappings, the latter which are equivalent to first-order Lipschitz mappings studied in this paper. The main result of this paper is to extend the Banach fixed point theorem (and an often-cited generalisation) to higher-order contraction mappings. We also present results on the problem of local Lipschitzity of these higher-order Lipschitz mappings. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of a common best proximity point for a pair of multivalued non-self mappings in partially ordered metric spaces. Also, we provide some interesting examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of $\alpha_{qs^{p}}$ -admissible mappings and provide some fixed point theorems involving this class of mappings satisfying some new conditions of contractivity in the setting of b-metric-like spaces. Our results extend, unify, and generalize classical and recent fixed point results for contractive mappings. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a unique common coupled fixed point theorem by using $(\psi , \alpha , \beta )$ -contraction in ordered partial metric spaces. We give an application to integral equations as well as homotopy theory. Also we furnish an example which supports our theorem. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced recently by Jleli and Samet (Fixed Point Theory Appl. 2015:33, 2015). [ABSTRACT FROM AUTHOR]

In this paper, we suggest some nonunique fixed results in the setting of various abstract spaces. The proposed results extend, generalize and unify many existing results in the corresponding literature. [ABSTRACT FROM AUTHOR]

Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space. [ABSTRACT FROM AUTHOR]

The paper deals with the achievement of introducing the notion of F-cone metric spaces over Banach algebra as a generalization of $N_{p}$ -cone metric space over Banach algebra and $N_{b}$ -cone metric space over Banach algebra and studying some of its topological properties. Also, here we define generalized Lipschitz and expansive maps for such spaces. Moreover, we investigate some fixed points for mappings satisfying such conditions in the new framework. Subsequently, as an application of our results, we provide an example. Our results generalize some well-known results in the 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]

In the paper general theorems on common fixed point for four mappings are presented. The results are compact and they extend and unify the respective part of the fixed point theory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, the set of common fixed points of a finite family of pseudo contraction mappings, and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a real Hilbert space. We establish results on the strong convergence of the sequence by the proposed scheme to a common element of the above three solution sets. These results extend and improve some corresponding results in this area. Finally, we give a numerical example which supports our main theorem. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some fixed point and common fixed point theorems for almost generalized $\mathcal{C}$-contractive mappings in an ordered complete metric space. Finally, two examples are given to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new notion of generalized α- ϕ-Geraghty proximal contraction mappings and investigate the existence of the best proximity point for such mappings in complete metric spaces. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. [ABSTRACT FROM AUTHOR]

Based on the concept of a $C^{*}$-algebra-valued b-metric space, this paper establishes some coupled fixed point theorems for mapping satisfying different contractive conditions on such space. As applications, we obtain the existence and uniqueness of a solution for an integral equation. [ABSTRACT FROM AUTHOR]

Very recently, Hussain et al. (Fixed Point Theory Appl. 2015:185, ) introduced the concept of JS-contraction and established some fixed point theorems for such contractions. In this paper, we introduce a new method of proofs that allows us to prove fixed point theorems for JS-contraction in complete metric spaces by removing two conditions in theorems of Hussain et al. Thus, we prove that fixed point Theorems 2.3-2.8 and Corollary 2.9 of Hussain et al. actually are consequences, and not generalizations, of the corresponding theorems of Ćirić, Chatterjea, Kannan, and Reich. [ABSTRACT FROM AUTHOR]

This paper aims to study the strong convergence of generalized modified Krasnoselskii iterative process for finding the minimum norm solutions of certain nonlinear equations with generalized strictly pseudocontractive, demiclosed, coercive, bounded, and potential mappings in uniformly convex Banach spaces. An application to nonlinear pseudomonotone equations is provided. The results extend and improve recent work in this direction. [ABSTRACT FROM AUTHOR]

In this paper, the notion of generalized probabilistic G-contractions in Menger probabilistic metric spaces endowed with a directed graph G is introduced and some new fixed point theorems for such mappings are established. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, and Piri and Kumam in Fixed Point Theory Appl. 2014:210, , etc.). Examples are provided to support the usability of our results. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of w-distances, and we prove existence theorems for single-valued mappings and set-valued mappings in a complete metric space which generalize Takahashi, Wong, and Yao's theorems. [ABSTRACT FROM AUTHOR]

In this paper, we study an interesting generalization of standard metric spaces, b-metric spaces, dislocated metric spaces, and modular spaces due to the recent work of Jleli and Samet. Here we modify the result for Ćirić quasi-contraction-type mappings and also prove the same result by taking D-admissible mappings. Moreover, we establish fixed point theorems for two well-known nonlinear contractions like rational contraction mappings and Wardowski type contraction mappings. Several important results in the literature can be derived from our results. Suitable examples are presented to substantiate our obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce first the concept of a Pompeiu-Hausdorff b-metric-like space. We also establish some best proximity points and stability results for controlled proximal contractive set valued mappings in the class of b-metric-like spaces and partial b-metric spaces. Moreover, we provide some examples and many nice consequences from our obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study iterative schemes for solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces and prove that the modified Mann iteration converges weakly to a common solution of the considered problems. Moreover, we present some examples and numerical results for the main results. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some fixed and common fixed point results for such mappings on modular spaces endowed with a graph. The existence of fixed and common points of mappings satisfying generalized contractive conditions of integral type is also obtained in such spaces. Some examples are presented to support the results obtained herein. Our results generalize and extend various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new classes of Hardy-Rogers type cyclic contractions and prove pertinent fixed point theorems for these Hardy-Rogers type contractions in the generating space of a b-dislocated metric family. [ABSTRACT FROM AUTHOR]

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due to Chidume and Ofoedu (J. Math. Anal. Appl. 333:128-141, ) in such a setting for the approximation of common fixed points of a finite family of total asymptotically nonexpansive mappings. As a consequence, we establish strong and △-convergence results which extend and generalize various corresponding results established in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new modified proximal point algorithm involving fixed point iterates of nonexpansive mappings in $\operatorname{CAT}(0)$ spaces and prove that the sequence generated by our iterative process converges to a minimizer of a convex function and a fixed point of mappings. [ABSTRACT FROM AUTHOR]