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We introduce two new classes of implicit relations S and S′ where S′ is a proper subset of S, and these classes are more general than the class of implicit relations defined by Altun and Simsek (2010). We prove the existence of coupled fixed points for the maps satisfying an implicit relation in S. These coupled fixed points need not be unique. In order to establish the uniqueness of coupled fixed points we use an implicit relation S′, where S′⊂S. Our results extend the fixed point theorems on ordered metric spaces of Altun and Simsek (2010) to coupled fixed point theorems and generalize the results of Gnana Bhaskar and Lakshimantham (2006). As an application of our results, we discuss the existence and uniqueness of solution of Fredholm integral equation.

The split common fixed point problem (also called the multiple-sets split feasibility problem) is to find a common fixed point of a finite family of operators in one real Hilbert space, whose image under a bounded linear transformation is a common fixed point of another family of operators in the image space. In the literature one can find many methods for solving this problem as well as for its special case, called the split feasibility problem. We propose a general method for solving both problems. The method is based on a block-iterative procedure, in which we apply quasi-nonexpansive operators satisfying the demi-closedness principle and having a common fixed point. We prove the weak convergence of sequences generated by this method and show that the convergence for methods known from the literature follows from our general result.

In this paper, we compare relation between n-tuple fixed point results and fixed point theorems in abstract metric spaces and metric-like spaces. Actually, we show that the results of n-tuple fixed point can be obtained from fixed point theorems and conversely. Thus, some recent results about both fixed points and n-tuple fixed points are equivalent against the claims of some authors.

In this paper, we prove coupled fixed point results for mappings without mixed monotone property in partially ordered G-metric spaces. Also we showed that if ( X , G ) is regular, these fixed point results holds.

In this paper, we establish a common fixed point theorem in semi-metric space with compatible mapping of type (E) which improves and extends similar known results in the literature.

In this paper we prove a common fixed point theorem of eight self mappings satisfying a generalized inequality using the concept of compatibility.

In this paper we prove a common fixed point theorem of compatible mappings of type (R). Our result modify the result of M. Koireng Meitei [4].

In this paper, we have derived certain coupled coincidence point and fixed point theorems in fuzzy metric spaces for coupled Kannan type mappings which we have defined here. The fuzzy metric space we have considered here is assumed to have a partial order defined on it. We have used Hadzic type t-norm. A common fixed point result follows from an additional assumption of the weak compatibility condition. Some coupled fixed point results in metric spaces are obtained by applications of the results proved in the context of fuzzy metric spaces. Our results are obtained without any assumption of continuity of the mappings. Some corollaries and three illustrative examples are given.

In this paper we present results regarding fixed point theory using notion of fuzzy orders.We propose an approach based on quasi metrics which in a way unifies the fixed point theory for ordered sets and metric spaces. is a map. A solution of such fixed point equations,when one exists,often has to be obtained by process of successive approximations.Order theory plays a role when X carries an order and when solution can be realized as joint of elements which approximates it. At some instances we find that fixed point theorems for ordered sets appear to be insufficient . In such cases , it is helpful to apply fixed point techniques in metric spaces. In this paper give some results in this direction. By using the notion of quasi metric spaces we prove a theorem simultaneously generalizing fixed point theorems for ordered structures and metric spaces.All results are interpreted in terms of fuzzy set theory.

In this paper, we prove coupled coincidence points and common fixed po ints theorem for two mappings satisfying various contractive conditions in partially ordered metric spaces. Our results will g eneralize and extend some recent results in fixed point theory.

In the renormalisation analysis of critical phenomena in quasi-periodic systems, a fundamental role is often played by fixed points of functional recurrences of the form \begin{equation*} f_{n}(x) = \sum_{i=1}^\ell a_i(x) f_{n_i} (\alpha_i(x)) \,, \end{equation*} where the $\alpha_i$, $a_i$ are known functions and the $n_i$ are given and satisfy $n-2 \le n_i \le n-1 $. We develop a general theory of fixed points of ``Composition Sum Operators'' derived from such recurrences, and apply it to test for fixed points in key classes of complex analytic functions with singularities. Finally we demonstrate the construction of the full space of fixed points of one important class, for the much studied operator \begin{equation*} Mf(x) = f(-\omega x) + f(\omega^2 x + \omega)\,, \quad \omega = (\sqrt{5}-1)/2\,. \end{equation*} The construction reveals previously unknown solutions., Comment: 19 pages; 1 figure

In the context of G -metric spaces we prove a common fixed point theorem for a sequence of self mappings using a new concept of α-series. Keywords: α-series, common fixed point, G -metric space Quaestiones Mathematicae 37(2014), 429-434

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.

The paper is basically concerned with interrelations between metric regularity and metric critical point theories. At the early stage of developments of regularity theory there was a feeling that every regularity criterion can be obtained with the help of a suitable (set-valued) contraction mapping principle. On the other hand, the assumptions of the well-known metric fixed point theorems (e.g., of Nadler (1969) or of Dontchev and Hager (1994)) imply metric regularity of the inverse mapping. The message of the paper is that, nonetheless, the theories are independent although the fundamental principles on which they are based have much in common. The first main result of the paper guarantees the existence of a fixed point if the contraction property holds only along the orbits of the mapping (rather than for arbitrary pairs of points in the feasible area) and actually only on some bounded pieces of the orbits determined by a certain “regularity horizon” condition. The bulk of the paper is devoted to the study of “two maps paradigm” when we have two set-valued mappings acting in opposite directions and we are interested in the existence of the so-called double fixed point. We consider two types of iteration procedures to get a fixed point, one based on simple Picard’s iterations and the other on the Lyusternik–Graves version of Newton’s method, that in principle may lead to different fixed points, although the impression is that estimates provided by the first procedure may be better. The paper is concluded by a discussion of the regularity problem for compositions of set-valued mappings. There are also quite a few examples in the paper.

In this paper $\lambda$-fuzzy approximate fixed point for a map and $\lambda$-fuzzy pair approximate fixed points for two maps in fuzzy metric spaces are defined. Instead of fuzzy numbers or real numbers are used to define fuzzy points. We also prove the existence theorems.

In this paper we have used a method of reducing coupled coincidence and coupled fixed point results in partially ordered metric spaces to the respective results for mappings with one variable, even obtaining (in some cases) more general theorems. Our results generalize, extend, unify and complement coupled coincidence point theorems established by Harjani et al. (2011) [18] and Razani and Parvaneh (2012) [26]. Also, by using this method several tripled coincidence and tripled common fixed point results in partially ordered metric spaces can be reduced to the coincidence and common fixed point results with one variable.

In this work, using the concepts of G-metric and b-metric we define a new type of metric which we call Gb-metric. We study some basic properties of such metric. We also prove a common fixed point theorem for six mappings satisfying weakly compatible condition in complete partially ordered Gb-metric spaces. A nontrivial example is presented to verify the effectiveness and applicability of our main result.

In this paper, we define non-Archimedean intuitionistic fuzzy metric space(Shortly, NIFMS), and prove a coupled fixed point theorems for map satisfying the mixed monotone property in partially ordered complete NIFMS.

Common fixed point theorems for two pairs of mappings are proved in dislocated fuzzy metric space using horizontally weak compatibility condition. Our results extends and generalises many existing fixed point theorems.

The object of this paper is to extend the concept of β-admissible for multivalued mappings due to Mohammadi et al. [B. Mohammadi, S. Rezapour and N. Shahzad, Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory and Applications 2013 (2013), 24] to fuzzy mappings and utilize this concept to prove a common α-fuzzy fixed point theorem for a pair of fuzzy mappings. We also give illustrative example which demonstrate the validity of the hypotheses of our results. Some related results to common fixed point for multivalued mappings are also derived from the main result.

The aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in symmetric spaces satisfying an implicit function. Some illustrative examples to highlight the realized improvements are furnished. Our results generalize and extend some recent results contained in Ali and Imdad [Sarajevo J. Math. 4(17)(2008), 269-285] to symmetric spaces and consequently a host of metrical common fixed theorems are generalized and improved. We state an integral type fixed point theorem in symmetric space. In the process, we also derive a fixed point result on common fixed point in probabilistic symmetric spaces.

In this paper, we use the mappings with quasi-contractive conditions, defined on a partially ordered set with cone metric structure, to construct convergent sequences and prove that the limits of the constructed sequences are the unique (common) fixed point of the mappings, and give their corollaries. The obtained results improve and generalize the corresponding conclusions in references.

Coupled fixed point theorems for a map satisfying mixed monotone property and a nonlinear, rational type contractive condition are established in a partially orderedG-metric space. The conditions for uniqueness of the coupled fixed point are discussed. We also present results for the existence of coupled coincidence points of two maps.

In this paper, we prove two fixed point theorems in S-metric spaces. Our results extend and improve some known results.

Using characteristic classes, we give an alternative proof for the fixed point property of C P 2 n .

In this paper we have proved some fixed point theorems in random fuzzy metric space for three mappings which satisfying some contractions. Also here we consider rational expression in contraction. INTRODUCTION AND PRILIMINARIES Probabilistic functional analysis has emerged as one of the important mathematical disciplines in view of its role in analyzing probabilistic models in the applied sciences. The study of fixed points of random operators forms a central topic in this area. The Prague school of probabilistic initiated its study in the 1950. However, the research in this area flourished after the publication of the survey article of Bharucha-Reid (3). Since then many interesting random fixed point results and several applications have appeared in the literature; for example the work of Beg and Shahazad

We prove a common fixed point theorem for a pair of mappings. Also, we prove a common fixed point theorem for pairs of self-mappings along with weakly commuting property.

In this paper, we prove some coupled coincidence point theorems for such nonlinear contraction mappings having a mixed monotone property in partially ordered metric spaces by dropping the condition of commutative. We also prove coupled common fixed point theorem for w-compatible mappings. An example of a nonlinear contraction mapping which is not applied by Lakshmikantham and Ciric’s theorem [1] but applied by our result is given. Further, we apply our results to the existence theorem for solution of nonlinear integral equations.

The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsik and J. Dobos [On a product of metric spaces, Math. Slovaca31 (1981) 193-205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsik and Dobos study was extended to the quasi-metric context in such a way that a general description of how to combine through a function a family of quasi-metrics in order to obtain a single one as output was provided by G. Mayor and O. Valero [Aggregation of asymmetric distances in Computer Science, Inform. Sci.180 (2010) 803-812]. In this paper, inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences, we have proved fixed point theorems for a new type of contractions, that we have called projective @F-contractions, defined between quasi-metric spaces that have been obtained via the so-called quasi-metric aggregation functions. Moreover, we show that the new fixed point results are useful to discuss, on the one hand, the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and, on the other hand, to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification.

In a spherically complete ultrametric space, a strictly contracting mapping has a fixed point. We indicate in this paper how this fixed point can either be reached or approximated.

We consider multivalued maps defined on a complete metric space endowed with a directed graph. We establish fixed point results for maps, called weak G -contractions, which send connected points into connected points and contract the length of paths. The fixed point sets are studied. The homotopical invariance property of having a fixed point is also established for a family of weak G -contractions.

In this paper we prove a triple coincidence point theorem for multi - valued and single-valued map- pings in a partially ordered metric space based on the concepts of (5). Also we give an example which supports our main result. Our result generalizes several results relating to coupled fixed point theorems.

Azam et al. (Numer Funct Anal Optim, 32(3):243–253, 2011) introduced a notion of complex valued metric space and obtained common fixed point result for mappings in such spaces. In this paper, introducing the concept of complex valued generalized metric spaces, some fixed and common fixed point results are obtained. As an application, periodic point property of common fixed point problem for two rational type contractive mappings involved therein is established.

In this paper, we first introduce a distance space and then give a new fixed point theorem for multi-valued contractions in such spaces. Even in the case of metric spaces, our main theorem unifies and generalizes some recent results in the literature. Some examples are given to show that the fixed point result given here is a genuine generalization.

The present paper is aimed at weakening the continuity conditions while proving fixed point theorems for a pair of maps and then using the results to provide applications in dynamic programming. Generalizing the concept of reciprocal continuity introduced by Pant (Indian J Pure Appl Math 30(2):147–152, 1999), we introduce the notion of g-reciprocal continuity and prove common fixed point theorems under minimal type contractive conditions. The results proved by us can be extended to the nonexpansive or Lipschitz type maps. Simultaneously, we provide more answers to the problem posed by Rhoades (Contemp Math 72:233–245, 1988) regarding existence a contractive definition which is strong enough to generate a fixed point, but which does not force the map to be continuous at the fixed point. We also provide an application of our results in dynamic programming.

We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.

We study the fixed point problem for a system of multivariate operators that are coordinate-wise uniformly monotone, in the setting of quasi-ordered sets. We show that this problem is equivalent to the fixed point problem for a mixed monotone operator that can be explicitly constructed. As a consequence, we obtain a criterion for the existence and uniqueness of solution to the considered problem, together with an approximating iterative scheme, in the setting of partially ordered metric spaces. As an application, we investigate a new abstract multidimensional fixed point problem. To validate our results, we also provide an application to a first-order differential system with periodic boundary value conditions.

First, we prove a common fixed point theorem using weakly compatible maps in 2-Menger space with t-norm of Hadzic type. Second, we prove a common fixed point theorem using the E.A. property along with weakly compatible maps. Further, we obtained a common fixed point theorem using the CLR property along with weakly compatible maps. At the end, we provide an application of our main theorem for four finite families of mappings.

This paper introduces economists to some fixed point theorems for discontinuous mappings with non-convex images on a non-convex domain. These theorems have recently been developed based on a new approach by mathematical economists and mathematicians. The new method of proof is first transformed into a sort of metatheorem, which is then used to obtain a set of necessary and sufficient conditions for a map to have a fixed point. Some fixed point theorems for discontinuous maps are then explained in more concrete cases. The formulations are intended for easier applications towards economic models involving discontinuity as well as non-convexity.

In this paper, we introduce a new, simple and unified approach to coupled and tripled fixed point theory. By using our method, we first give a new coupled fixed point theorem. Then, we use our technique to present a new tripled fixed point result. As an application, we discuss the existence and uniqueness for solution of an initial value problem. Our results extend and improves some recent results in literature.

It is shown that monotone property in fixed point results for mappings in partially ordered metric spaces can be replaced by a weaker property which is often easy to check. Consequently, these results can be applied in a much wider class of problems

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed $g$-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

The purpose of this paper is to present a fixed point theorem due to Dass and Gupta (Indian J Pure Appl Math 6:1455–1458, 1975) in the context of partially ordered metric spaces.

A consequence of a logic program under answer set semantics is one that is true for all answer sets. This article considers using loop formulas to compute some of these consequences in order to increase the efficiency of answer set solvers. Since computing loop formulas are in general intractable, we consider only loops with either no external support or at most one external support, as their loop formulas are either unit or binary clauses. We show that for disjunctive logic programs, loop formulas of loops with no external support can be computed in polynomial time, and that an iterative procedure using unit propagation on these formulas and the program completion computes the well-founded models in the case of normal logic programs and the least fixed point of a simplification operator used by DLV for disjunctive logic programs. For loops with at most one external support, their loop formulas can be computed in polynomial time for normal logic programs, but are NP-hard for disjunctive programs. So for normal logic programs, we have a procedure similar to the iterative one for loops without any external support, but for disjunctive logic programs, we present a polynomial approximation algorithm. All these algorithms have been implemented, and our experiments show that for certain logic programs, the consequences computed by our algorithms can significantly speed up current ASP solvers cmodels, clasp, and DLV.

In this paper, we introduce the new notion of g-monotone mapping and prove some fixed point theorems for multi-valued and single-valued g-increasing mappings in partially ordered metric spaces. The mappings considered in this paper are assumed to satisfy certain metric inequalities which are established by an altering distance function. The presented results extend and improve the main results of Choudhury and Metiya [B.S. Choudhury, N. Metiya, Multi-valued and single-valued fixed point results in partially ordered metric spaces, Arab J. Math. Sci. 17 (2011) 135–151].

In this paper, we introduce a new class Γ, which is weak than a known class Ψ, of real continuous functions defined on [0, +∞), and use another method to prove the known unique common fixed point theorem for four mappings with γ-contractive condition instead of Ψ-contractive condition on 2-metric spaces.

In recent times the fixed point results in partially ordered metric spaces has greatly developed. In this paper we prove common fixed point results for multivalued and singlevalued mappings in partially ordered metric space. Our theorems generalized the theorem in [1] and extends the many more recent results in such spaces.