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In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and Δ-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasinonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in Table 1. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces. [ABSTRACT FROM AUTHOR]

Recently, Jleli et. al. [9] introduced by the concept of a (H, ψ)-fixed point, and they establish some fixed point results for various classes of operators defined on a metric space (M, d). This study is devoted to investigate the problem whether the existence and uniqueness of integral type (H, ψ)F-contraction mappings on complete metric space. At the end, we give an illustrative example. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a fractal of generalized Θ-Hutchinson Operator with the help of a finite family of Θ-contraction mappings, a class of mappings more general than contractions, defined on a complete metric space. Our results unify, generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

We introduce a new pair of mappings (S , T) on D * -metric spaces called D S * -W.C. and D R S * -W.C. Many examples are presented to show the difference between these mappings and other types of mappings in the literature. Moreover, we obtain several common fixed point results by using these types of mappings and the (E.A) property. We then employ the fixed point results to establish the existence and uniqueness of a solution for a class of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

This paper is a brief review of results in the theory of covering mappings of metric spaces and vector metric spaces and its applications to implicit differential equations. For the Cauchy problem and boundary-value problems, we obtain existence conditions, estimates of solutions, and conditions of the continuous dependence of solutions on the parameters of the equation and initial and boundary conditions. [ABSTRACT FROM AUTHOR]

Given a set-valued nonexpansive mapping which acts on a metric space, we study the convergence of its inexact iterates to its attracting sets in the case where the errors are summable. In particular, we extend results which are known to hold for single-valued nonexpansive self-mappings of metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to obtain new fixed-disc results on metric spaces. To do this, we present a new approach using the set of simulation functions and some known fixed-point techniques. We do not need to have some strong conditions such as completeness or compactness of the metric space or continuity of the self-mapping in our results. Taking only one geometric condition, we ensure the existence of a fixed disc of a new type contractive mapping. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of extended parametric b-metric space and investigate the existence of fixed points for some contractive type mappings in such spaces. Consequently, we derive some new fixed point results in triangular ordered extended fuzzy b-metric spaces. Moreover, some examples and an application are provided here to illustrate the applicability of the obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this article, we consider the existence of a unique best proximity point x* ∊ A such that d(x*, Tx*) = dist(A,B) for generalized φ-weak contraction mapping T : A → B, where A,B(≠, θ) are subsets of a metric space (X, d). [ABSTRACT FROM AUTHOR]

A new Caristi-type inequality is considered and Caristi's fixed point theorem for mappings of complete metric spaces is developed (in both the single- and set-valued cases). On the basis of this development mappings of complete metric spaces which are contractions with respect to a function of two vector arguments are studied. This function is not required to be a metric or even a continuous function. The proved theorems are generalizations of the Banach contraction principle and Nadler's theorem. [ABSTRACT FROM AUTHOR]

In this paper, a general common fixed point theorem for two pairs of subcompatible mappings satisfying integral type implicit relations is obtained in a metric space. Our result improves several results especially the result of Pathak et al. [6]. Also, another common fixed point theorem of Greguš type for four mappings satisfying a contractive condition of integral type in a metric space using the concept of subcompatibility is established which generalizes the result of Djoudi and Aliouche [1] and others. Again a third common fixed point theorem for two pairs of near-contractive subcompatible mappings is given which enlarges the result of Mbarki [5] and references therein. [ABSTRACT FROM AUTHOR]

In this paper, a general coincidence and common fixed points theorem for two hybrid pairs of mappings satisfying property (E.A) is proved, generalizing the main results from [3] and [9]. [ABSTRACT FROM AUTHOR]

We introduce a pseudometric TV on the set M X of all functions mapping a rectangle X on the plane R 2 into a metric space M , called the total joint variation. We prove that if two sequences { f j } and { g j } of functions from M X are such that { f j } is pointwise precompact on X , { g j } is pointwise convergent on X with the limit g ∈ M X , and the limit superior of TV ( f j , g j ) as j → ∞ is finite, then a subsequence of { f j } converges pointwise on X to a function f ∈ M X such that TV ( f , g ) is finite. One more pointwise selection theorem is given in terms of total ε -variations ( ε > 0 ), which are approximations of the total variation as ε → 0 . [ABSTRACT FROM AUTHOR]

In this paper, we prove some results on the existence of fixed points for multivalued maps with respect to general distance. Our results improve and generalize a number of known fixed point results including the fixed point results [ABSTRACT FROM AUTHOR]

We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent fixed point and best proximity point results. [ABSTRACT FROM AUTHOR]

We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application. [ABSTRACT FROM AUTHOR]

In this paper we prove some general fixed point theorems for mappings satisfying (E.A.)-property. The proved results generalize and extend various known results in the literature. As a consequence, a fixed point theorem for mappings satisfying a contractive condition of integral type is obtained. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to give some results related to classes of mappings, known as (m, p)-(hyper)expansive and (m, p)-(hyper)contractive acting on a metric space X. A mapping T : X → X is (m, p)-expansive ( respectively, (m, p)-contractive) for some metric d, integer m ⩾ 1 and p 2 (0, ∞) if, for any x, y ϵ X; Σ(-1)k(m/k)d(Tkx,Tky)p⩽0(respectively, ⩾ 0 ) ok⩽⩽land it is (m, p)-hyperexpansive ( respectively, (m, p)-hypercontractive) if, for all x, y ∊ X Σ(-1)k (l/k) d ( Tkx, Tky )p ⩽ 0 (respectively, ⩾ 0 ), for l ∊ {1, 2, ...,mg}.ok⩽⩽l The notions of (m; p)-expansive mapping or of (m; p)-contractive mapping on a metric space generalize the notion of m-isometry for bounded linear operators acting on Hilbert or Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results for generalized con-tractive multimaps with respect to generalized distance. Consequently, several known fixed point results either generalized or improved including the corresponding recent fixed point results of Ciric, BinDehaish-Latif, Latif-Albar, Klim-Wardowski, Feng-Liu. [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 the first half of the paper, we are concerned with the problems of existence (and searching) of coincidence points and the common preimage of a closed subset (in particular, a common root) in the case of a finite system of mappings of one metric space to another one. The second half of the paper is devoted to fiberwise variants of Arutyunov's theorem on coincidence points. Obtaining the main results of the paper is based on the use of the class of almost exactly ( α , β ) -search functionals that is wider than Fomenko's class of ( α , β ) -search functionals. [ABSTRACT FROM AUTHOR]

In this study, we embed a metric space endowed with a convex combination operation, which is called a convex combination space, into a Banach space, where the embedding preserves the structures of the metric and convex combination. We also establish applications of this embedding for a random element that takes values in this type of space. On the one hand, we show some useful properties of mathematical expectation, such as the representation of expectation through continuous affine mappings and the linearity of expectation. On the other hand, the notion of conditional expectation is also introduced and discussed. Using this embedding theorem, we establish some basic properties of conditional expectation, Jensen's inequality, the convergences of martingales, and ergodic theorem. [ABSTRACT FROM AUTHOR]

E. R. Avakov, A. V. Arutyunov, S. E. Zhukovskiĭ, and E. S. Zhukovskiĭ studied the problem of Lipschitz perturbations of conditional coverings of metric spaces. Here we propose some extension of the concept of conditional covering to vector-valued mappings; i.e., the mappings acting in products of metric spaces. The idea is that, to describe a mapping, we replace the covering constant by the matrix of covering coefficients of the components of the vector-valued mapping with respect to the corresponding arguments. We obtain a statement on the preservation of the property of conditional and unconditional vectorial coverings under Lipschitz perturbations; the main assumption is that the spectral radius of the product of the covering matrix and the Lipschitz matrix is less than one. In the scalar case this assumption is equivalent to the traditional requirement that the covering constant be greater than the Lipschitz constant. The statement can be used to study various simultaneous equations. As applications we consider: some statements on the solvability of simultaneous operator equations of a particular form arising in the problems on n-fold coincidence points and n-fold fixed points; as well as some conditions for the existence of periodic solutions to a concrete implicit difference equation. [ABSTRACT FROM AUTHOR]

Fixed point theory is very wide field, which have many applications in different areas. The concept of altering distance to find fixed point results have been explored by many authors. In the present paper, we achieve unique common fixed point results for two self-mappings using a generalization of altering distance and a rational type contractive condition. An example has also been given in support of our result. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the notion of the common limit range property, we prove some new integral type common fixed point theorems for weakly compatible mappings satisfying a $$\varphi $$ -weak contractive condition in metric spaces. Moreover, we extend our results to four finite families of self mappings, and furnish an illustrative example and an application to support our main theorem. Our results improve, extend, and generalize well-known results on the topic in the literature. [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]

We prove Theorem 1.3 of [] under a more general situation and rectify some typographic errors that appear in the paper. [ABSTRACT FROM AUTHOR]

Let $(X,d)$ be a metric space and $J: X\rightarrow2^{X}$ be a multivalued mapping. In this work, we discuss the definition of G-contraction mappings introduced by Beg et al. (Comp. Math. Appl. 60:1214-1219, 2010) and show that it is restrictive and fails to give the main result of (Beg et al. in Comp. Math. Appl. 60:1214-1219, 2010). In this work, we give a new definition of the G-contraction and obtain sufficient conditions for the existence of fixed points for such mappings. [ABSTRACT FROM AUTHOR]

In this paper the large scale structure of R is investigated and two kinds of non-coarse equivalent subsets of R are characterized. In addition L-spaces and H-spaces in arbitrary metric spaces are introduced and it is shown that they are not coarse equivalent. [ABSTRACT FROM AUTHOR]

We prove common fixed point theorems in metric spaces for expansive mappings satisfying an implicit relation without non-decreasing assumption and surjectivity using the concept of weak compatibility which generalize some theorems appearing in the recent literature. [ABSTRACT FROM AUTHOR]

In the present paper a general fixed point theorem for two pairs of occasionally weakly compatible mappings is proved. This theorem generalizes some results by metric spaces, symmetric spaces, quasi - metric spaces, b - metric spaces, generalized metric spaces, G - metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of coincidence points for nonlinear mappings of any number of arguments under a weak (ψ,φ) -contractive condition. Our results generalize, extend and unify several classical and very recent related results in the literature (see Aydi et al. (2011), Berinde (2010), Gnana-Bhaskar and Lakshmikantham (2006), Berzig and Samet (2012), Borcut and Berinde (2012), Choudhury et al. (2011), Karapınar and Luong (2012), Lakshmikantham and Ćirić (2009), Luong and Thuan (2011), Roldán (2012)). [ABSTRACT FROM AUTHOR]

In this paper a general fixed point theorem for mappings satisfying an implicit relation is proved for two pairs of mappings with a common (E.A) - property, which generalize the main results from [1]. In the last part of the paper, as applications we obtain some fixed point results for mappings satisfying contractive condition of integral type, for almost contractive mappings and for (ψ, φ) - weakly contractive mappings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend Mizoguchi–Takahashi's fixed point theorem for multi-valued mappings on a metric space endowed with a graph. As an application, we establish a fixed point theorem on an ε-chainable metric space for mappings satisfying Mizoguchi–Takahashi contractive condition uniformly locally. Also, we establish a result on the convergence of successive approximations for certain operators (not necessarily linear) on a Banach space as another application. Consequently, this result yields the Kelisky–Rivlin theorem on iterates of the Bernstein operators on the space and also enables us study the asymptotic behaviour of iterates of some nonlinear Bernstein type operators on . [Copyright &y& Elsevier]

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 article, we prove the existence of a best proximity point for F-contractive nonself mappings and state some results in the complete metric spaces. Also we define two kinds of F-proximal contraction and extend some best proximity theorems and improve the recent results. [ABSTRACT FROM AUTHOR]

We prove in this paper a general fixed point theorem for two pairs of hybrid mappings involving altering distances and satisfying implicit relations, generalizing the recent results from [29]. As application, a general fixed point theorem for two hybrid pairs of mappings of integral type is obtained. In particular cases, new results for almost contractive hybrid of Berinde type and φ - contractive hybrid of Matkowski types are obtained. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of fixed points for mappings defined on complete metric spaces, satisfying a general contractive inequality depending on two additional mappings. [ABSTRACT FROM AUTHOR]

We consider a broad class of fair leader election algorithms, and study the duration of contestants (the number of rounds a randomly selected contestant stays in the competition) and the overall cost of the algorithm. We give sufficient conditions for the duration to have a geometric limit distribution (a perpetuity built from Bernoulli random variables), and for the limiting distribution of the total cost (after suitable normalization) to be a perpetuity. For the duration, the proof is established via convergence (to 0) of the first-order Wasserstein distance from the geometric limit. For the normalized overall cost, the method of proof is also convergence of the first-order Wasserstein distance, augmented with an argument based on a contraction mapping in the first-order Wasserstein metric space to show that the limit approaches a unique fixed-point solution of a perpetuity distributional equation. The use of these two steps is commonly referred to as the contraction method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new notion of almost Ψ-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the (G,ψ)-contraction and the (G,ψ)-graphic contraction in a metric space by using a graph. We explain some conditions for a mapping which is a (G,ψ)-contraction to have a unique fixed point and also we give conditions as regards the existence of a fixed point for (G,ψ)-graphic contraction by applying the connectivity of the graph in both cases. Moreover, we give examples to show that our results are a substantial improvement of some known results in the literature. [ABSTRACT FROM AUTHOR]

Let (X, ≤) be a partially ordered set and d be a metric on X such that (X; d) is a complete metric space, g : X → X be a mapping. In the paper, we introduce a new concept of mixed comparable property with respect to g, and obtain some tripled coincidence point theorems for such a class of mappings with this property. Our results generalize and extend the work of V. Berinde and M. Borcut [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889{4897]. Moreover, some examples are given to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we show that some examples in (Mursaleen et al. in Fixed Point Theory Appl. 2012:124, 2012) are not correct. Then, we extend, improve and generalize their results. Finally, we state some examples to illustrate our obtained results. MSC: 47H10, 54H25. [ABSTRACT FROM AUTHOR]

This paper is concerned with a generalized Ky Fan's inequality. We first give an existence result of generalized Ky Fan's (weak) efficient points, and then establish a complete metric space. Based on these results, we obtain the sufficient and necessary conditions of upper semicontinuity of efficient solution mapping to a generalized Ky Fan's inequality. We also obtain the sufficient conditions of lower semicontinuity and continuity of efficient solution mapping to a generalized Ky Fan's inequality. Our results are new and different from the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a notion of coincidence point between mappings in any number of variables and we prove some existence and uniqueness fixed point theorems for nonlinear mappings verifying different kinds of contractive conditions and defined on partially ordered metric spaces. These theorems extend and clarify very recent results that can be found in [T. Gnana-Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7)(2006) 1379–1393], [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889–4897] and [M. Berzig, B. Samet, An extension of coupled fixed point’s concept in higher dimension and applications, Comput. Math. Appl. 63 (8) (2012) 1319–1334]. [Copyright &y& Elsevier]

In this paper, we introduce the concept of T-asymptotically regular mapping and establish a lemma for ε-fixed points of two commuting mappings in metric spaces. This lemma is used for proving approximate fixed point theorems for various types of contraction mappings in the framework of metric spaces. Our results in this paper extends and improves upon, among others, the corresponding results of Berinde given in [2]. [ABSTRACT FROM AUTHOR]

In this paper, we establish fixed point theorems for contractive mappings on a metric space endowed with an amorphous binary relation. The presented theorems extend and generalize many existing results on metric and ordered metric spaces. We apply also our main result to derive fixed point theorems for cyclical contractive mappings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce some new types of pairs of mappings on -metric spaces called -weakly commuting of type and -weakly commuting of type . We obtain also several common fixed point results by using the (E.A) property. [Copyright &y& Elsevier]

Abstract: A k-dissimilarity map on a finite set X is a function assigning a real value to each subset of X with cardinality k, . Such functions, also sometimes known as k-way dissimilarities, k-way distances, or k-semimetrics, are of interest in many areas of mathematics, computer science and classification theory, especially 2-dissimilarity maps (or distances) which are a generalisation of metrics. In this paper, we show how regular subdivisions of the kth hypersimplex can be used to obtain a canonical decomposition of a k-dissimilarity map into the sum of simpler k-dissimilarity maps arising from bipartitions or splits of X. In the special case , this is nothing other than the well-known split decomposition of a distance due to Bandelt and Dress [H.-J. Bandelt, A.W.M. Dress, A canonical decomposition theory for metrics on a finite set, Adv. Math. 92 (1992) 47–105], a decomposition that is commonly to construct phylogenetic trees and networks. Furthermore, we characterise those sets of splits that may occur in the resulting decompositions of k-dissimilarity maps. As a corollary, we also give a new proof of a theorem of Pachter and Speyer [L. Pachter, D.E. Speyer, Reconstructing trees from subtree weights, Appl. Math. Lett. 17 (2004) 615–621] for recovering k-dissimilarity maps from trees. [Copyright &y& Elsevier]