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The purpose of this paper is to prove some common fixed point theorems in S-metric spaces for a pair of self-mappings which is weakly compatible satisfying an implicit relation and give some consequences of the main result. We also give some examples to demonstrate the validity of the results and an application of the main result. The results presented in this paper generalize, extend and enrich several results in the existing literature. It specially generalize the results of Imdad et al. [10] from metric space to the setting of S-metric space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study composite implicit iterative process with errors for two finite families of non-Lipschitzian asymptotically quasi-nonexpansive type mappings. In this paper, we have obtained a necessary and sufficient condition to converge to common fixed points for proposed scheme and mappings and also obtained a strong convergence theorem by using Condition (B') in the framework of real Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, a fixed point theorem for L-fuzzy set-valued map defined on a complete metric space is established by taking a general contractive inequality. It is shown herein that a few known significant metric fixed point theorems in the framework of fuzzy set-valued and multivalued mappings can be easily followed from our main result. A nontrivial example is provided to validate the hypotheses of our established idea. From application point of view, we study solvability conditions of a class of functional equations arising in dynamic programming, by using the techniques of L-fuzzy set-valued maps. [ABSTRACT FROM AUTHOR]

In this paper, we consider, discuss, complement, improve and enrich some results of Perov type. By using the method of c-sequences we get much shorter proofs, then ones in the literature with the Perov type theorems. Among other things we establish new fixed point results for the mappings of Perov type which are generalized contractions in the sense of Ćiric type. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present best proximity point results of (α, Ψ)- proximal contractive type mappings on a closed ball in complete metric spaces. An example was constructed to validate the results proved herein. As an application, we derive best proximity result in the setup of complete metric spaces endowed with binary relation. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of generalised rational α-Meir-Keeler contraction mappings on rectangular b-metric spaces. The existence and uniqueness of fixed points are also examined. Consequences are also discussed. [ABSTRACT FROM AUTHOR]

In this paper a general fixed point theorem for mappings satisfying an implicit relation is proved. This result generalize Theorem 2.2 [1]. In the last part of the paper we prove that these mappings satisfy property (P). [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for new classes of contractive mappings which are generalizations of the A-contractions of Akram et al. Indeed, our results improve, generalize and extend the results of Fisher, Jungck and the recent results of Akram et al. In actual fact, our results unify several other classical results in the literature concerning the fixed point and the common fixed point settings. [ABSTRACT FROM AUTHOR]

In this paper, we study a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some weak convergence theorems for mentioned scheme and mappings in uniformly convex Banach spaces. Our results extend and generalize the corresponding results recently announced by Wei and Guo [16] and many others. [ABSTRACT FROM AUTHOR]

In this paper, we use a class of convex-power condensing mappings with respect to a measure of weak noncompactness in Banach spaces in order to present a new Krasnosel'skii fixed point theorem for multivalued mappings which have sequentially closed graph. We prove also a new version of Leary-Schauder type results. We apply these results to investigate the existence of weak solution to a Volterrra integral inclusion of Krasnosel'skii type in a non reflexive Banach space. [ABSTRACT FROM AUTHOR]

In this paper, by using the concept of proximal admissible mappings, we discus the existence of best proximity points for new class of non-self mappings satisfying a nonlinear contraction involving a new class of functions in the setting of partial ordered metric spaces. We show that many known results in the literature are simple consequences of our obtained results. We also provide some concrete examples illustrating the obtained results. [ABSTRACT FROM AUTHOR]

We suggest and analyze an iterative method to approximate a common solution of a combination of split general variational-like inequality problems and a common fixed point problem for a family of generalized asymptotically nonexpansive nonself mappings by using a specific way of choosing the indexes of the involved mappings. Further, we prove that sequences generated by the proposed iterative algorithm converge strongly to a common solution of these problems. The results presented in this paper generalize and unify some known related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove a common fixed point for two pairs of self mappings, which are weakly subsequentially continuous and compatible of type (E) by using the notion of C-function, two examples and an application for the existence of solution of systems functional equations are given to illustrate and support our results. [ABSTRACT FROM AUTHOR]

Adrian, Ioan, Hussain and Shah introduced ordered L-spaces and cone bmetric spaces, respectively (see [B.S. Choudhury, N. Metiya: Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134(2005), No. 2, 411-418] and [N. Hussian, M.H. Shah: KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62(2011), 1677-1684], respectively). The former obtained the unique fixed point theorems in ordered L-spaces, while the latter got some topological properties of cone b-metric spaces. Following Adrian, Ioan, Hussain and Shah, the present paper will show unique fixed point results for self-mappings which do not satisfy the continuity and monotonicity in ordered cone b-metric spaces without the assumption of normality, where the coefficient s satisfies s = 1. Our main results improve and generalize some related results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduced the concept of integral type contractive condition for weak commutive mappings in multiplicative metric spaces. Also we give an example. [ABSTRACT FROM AUTHOR]

The aim of this paper is to unify several fixed and coincidence point results satisfying (ψ, φ)-weakly contractive conditions via C-class functions in the framework of partially ordered generalized metric spaces. As an application of our results, coincidence point of mappings satisfying integral type contractive conditions is also obtained. Some examples are provided to support the results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to give a generalization of results presented by Long et al. (Fixed Point Theory Appl. 2014:117, 2014) in the framework of partial metric spaces. Three examples are given to support our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions of both variational inequality problems and mixed variational inequality problems on Hadamard manifolds. We also introduce the proximal point algorithm to solve mixed variational inequality problems on these spaces. Our results and ideas may stimulate further research in this fascinating and interesting field of research. [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 establish some strong and weak convergence results of modified S-iteration process for two generalized asymptotically quasi-nonexpansive non-self mappings in the framework of Banach spaces. Our results extend and generalize the previous works from the current existing literature. [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]

Recently, Abbas et al. [M. Abbas, L. Ćirić, B. Damjanović M.A. Khan: Coupled coincidence and common fixed point theorems for hybrid pair of mappings, Fixed Point Theory Appl., 2012, 2012:4, 11 pages] obtained coupled coincidence and common fixed point of a hybrid pair of mappings satisfying a nonlinear contractive condition in a complete metric space. In this paper, some coupled coincidence and common fixed point results for two hybrid pairs of multivalued and single valued mappings are obtained. Our results unify, generalize, and complement various known comparable results from the current literature. We also provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of α-Caristi type multivalued contraction mappings and prove fixed point theorems for such mappings on complete metric space. We also construct some examples to illustrate our result. As consequence of our results we get some more interesting fixed point theorems. [ABSTRACT FROM AUTHOR]

In this paper we obtain the common fuzzy fixed points of sequence of mappings satisfying Edelstein type contractive conditions in a metric linear space by using iterations. In the process we have generalized several well known recent and classical results. [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 generalize the notion of modular metric spaces in the sense of Czerwik [S. Czerwik: Contraction mappings in b-metric spaces, ActaMath. Inf. Univ. Ostraviensis, 1(1993), 5-11] and obtain the notion of modular b-metric spaces. We also prove fixed point theorems for mapping satisfying contractive type condition defined on modular b-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we modify the projection algorithm proposed by [Y. Liu: Weak convergence of a new projection algorithm for variational inequalities in Banach spaces, Nonlinear Funct. Anal. Appl., 21(2016), 121-129] for solving a variational inequality problem involving a monotone and Lipschitz continuous mapping in Banach spaces. The purpose of this modification is to change the implicit iterative method to an explicit iterative method. The latter is easier to compute. We obtain a weak convergence theorem. [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]

In this paper, we generalize the notion of α- ψ-contractive type mappings by introducing (α, ψ, ϕ)-contractive mappings. Further, we prove a fixed point theorem for (α, ψ, ϕ)-contractive mappings on a space with two metrics. Our result also generalizes some known results in literature. [ABSTRACT FROM AUTHOR]