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The aim of this paper is to study the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite collection of generalized cyclic Γ-contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature. [ABSTRACT FROM AUTHOR]

In this article, we present a completeness characterization of b ∼ metric space via existence of fixed points of generalized multivalued quasicontractions. The purpose of this paper is twofold: (a) to establish the existence of fixed points of multivalued quasicontractions in the setup of b ∼ metric spaces and (b) to establish completeness of a b ∼ metric space which is a topological property in nature with existence of fixed points of generalized multivalued quasicontractions. Further, a comparison of our results with comparable results shows that the results obtained herein improve and unify the existing results in the literature applicable to the case where existing results fail. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce generalized Suzuki type F-contraction fuzzy mappings and to prove the existence of fixed fuzzy points for suchmappings in the setup of complete ordered metric spaces. An example is provided to show the validity of our results, followed by couple of remarks about the comparison of obtained results with the existing results in the literature. An application of our result to the domain of words is also presented. [ABSTRACT FROM AUTHOR]

It is our purpose in this paper to prove some fixed point results and Fejer monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type Volterra-Fredholm functional nonlinear integral equation in complex valued Banach spaces. [ABSTRACT FROM AUTHOR]

T. Zamfirescu, [Fixed point theorems in metric spaces, Arch. Math. (Basel), 23 (1972), 292-298] obtained a very interesting fixed point theorem on complete metric spaces, by combining results of Banach, Kannan and Chatterjea. In this paper, we introduce the concept of Zamfirescu- Perov type cyclic contraction and obtain best proximity point theorems for such mapping in the frame work of regular cone metric spaces. Examples are given to support our results. Our results extend and generalize several comparable existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce the concept of Suzuki type multivalued (θ,R)-contraction and we will prove some fixed point results in the setting of a metric space equipped with a binary relation. Our results generalize and extend various comparable results in the existing literature. Examples are provided to support the results proved here. As an application of our results, we obtain a homotopy result, proving the existence of a solution for a second-order differential equation and for a first-order fractional differential equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce Ciric-Suzuki type quasi-contractive multivalued operators and to obtain the existence of fixed points of such mappings in the framework of b-metric spaces. Some examples are presented to support the results proved herein. We establish a characterization of strong b-metric and b-metric spaces completeness. An asymptotic estimate of a Hausdorff distance between the fixed point sets of two Ciric-Suzuki type quasi-contractive multivalued operators is obtained. As an application of our results, existence and uniqueness of multivalued fractals in the framework of b-metric spaces is proved. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of common fixed points of multivalued Perov type contractionmappings on conemetric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notion of complex valued fuzzy metric spaces. We prove some fixed point results of contractive mappings on complex valued fuzzy metric spaces. Some examples are presented to support the results proved herein. Our results extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, common fixed point for four maps using an implicit contractive condition in a complete metric space is proved. Some periodic point results for such mappings are also obtained. These results extend and generalize several comparable results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we study sufficient conditions to find a vertex v of a graph such that Tv is a terminal vertex of a path which starts from v, where T is a self graphic contraction transformation defined on the set of vertices. Some examples are presented to support the results proved herein. Our results widen the scope of various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of α-dominated multivalued mappings and establish the existence of common fixed points of such mappings on a closed ball contained in left/right K-sequentially complete dislocated quasi b-metric spaces. These results improve, generalize, extend, unify, and complement various comparable results in the existing literature. Our results not only extend some primary results to left/right K-sequentially dislocated quasi b-metric spaces but also restrict the contractive conditions on a closed ball only. Some examples are presented to support the results proved herein. Finally as an application, we obtain some common fixed point results for single-valued mappings by an application of the corresponding results for multivalued mappings satisfying the contractive conditions more general than Banach type and Kannan type contractive conditions on closed balls in a left K-sequentially complete dislocated quasi b-metric space endowed with an arbitrary binary relation. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to deal with some properties of interest in two types of fuzzy ordered proximal contractions of cyclic self-mappings T integrated in a pair (g, T) of mappings. In particular, g is a non-contractive fuzzy self-mapping, in the framework of non-Archimedean ordered fuzzy complete metric spaces and T is a p-cyclic proximal contraction. Two types of such contractions (so called of type I and of type II) are dealt with. In particular, the existence, uniqueness and limit properties for sequences to optimal fuzzy best proximity coincidence points are investigated for such pairs of mappings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce α-proximal fuzzy contraction of type-I and II in complete fuzzy metric space and obtain some fuzzy proximal and optimal coincidence point results. The obtained results further unify, extend and generalize some already existing results in literature. We also provide some examples which show the validity of obtained results and a comparison is also given which shows that contractive mappings and obtained results further generalizes already existing results in literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present fixed point results of convex contraction, convex contraction of order 2, weakly Zamfirescu and Ćirić strong almost contraction mappings in the framework of G-metric spaces. Some examples are presented to support the results proved herein. As an application, we derive Suzuki type fixed point in G-metric spaces. Our results generalize and extend various results in the existing literature. We also present some examples to illustrate our new theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new contraction called dualistic contraction of rational type and used it to obtain some fixed point results in ordered dualistic partial metric spaces. These results generalize various comparable results appeared in the literature. We provide an example to show the usefulness of our results among corresponding fi xed point results proved in metric spaces. [ABSTRACT FROM AUTHOR]

This paper discusses some convergence properties in fuzzy ordered proximal approaches defined by $$\{ (g_{n} ,T_{n} )\}$$ -sequences of pairs, where $$g:A \to A$$ is a surjective self-mapping and $$T:A \to B,$$ where Aand Bare nonempty subsets of and abstract nonempty set X and $$(X,\,M,\, * ,\,\underline{ \prec } )$$ is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metric M, a triangular norm * and an ordering $$\underline{ \prec } .$$ The fuzzy set M takes values in a sequence or set $$\{ M_{{\sigma_{n} }} \}$$ where the elements of the so-called switching rule $$\{ \sigma_{n} \} \subset \varvec{Z}_{ + }$$ are defined from $$X \times X \times \varvec{Z}_{0 + }$$ to a subset of $$\varvec{Z}_{ + } .$$ Such a switching rule selects a particular realization of M at the nth iteration and it is parameterized by a growth evolution sequence $$\{ \alpha_{n} \}$$ and a sequence or set $$\{ \psi_{{\sigma_{n} }} \}$$ which belongs to the so-called $$\varPsi (\sigma ,\alpha )$$ -lower-bounding mappings which are defined from [0, 1] to [0, 1]. Some application examples concerning discrete systems under switching rules and best approximation solvability of algebraic equations are discussed. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present fuzzy optimal coincidence point results of fuzzy proximal quasi contraction and generalized fuzzy proximal quasi contraction of type-1 in the framework of complete non-Archimedean fuzzy metric space. Some examples are presented to support the results which are obtained here. These results also hold in fuzzy metric spaces when some mild assumption is added to the set in the domain of mappings which are involved here. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of cyclic R-contraction mapping and then study the existence of fixed points for such mappings in the framework of metric spaces. Examples and application are presented to support the main result. Our result unify, complement, and generalize various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized almost rational contraction with respect to a pair of self mappings on a complete metric space. Several common fixed point results for such mappings are proved. Our results extend and unify various results in the existing literature. An example and application to obtain the existence of a common solution of the system of functional equations arising in dynamic programming are also given in order to illustrate the effectiveness of the presented results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present coincidence best proximity point results of F g-weak contractive mappings in partially ordered metric space. Some examples are presented to prove the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce best proximal contractions in complete ordered non-Archimedean fuzzy metric space and obtain some proximal results. The obtained results unify, extend, and generalize some comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of parameters is a finite set. We then show that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduced from comparable existing results. We also present some examples to validate and illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of common fixed points of multivalued F-contraction mappings on a metric space endowed with a graph. An example is presented to support the results proved herein. Our results unify, generalize and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

We present fixed point results of mappings satisfying generalized contractive conditions in complex valued metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of generalized contractive-type mappings involved in cocyclic representation of a nonempty subset of a complex valued metric space are also obtained. Some examples are also presented to support the results proved herein. These results extend and generalize many results in the existing literature. [ABSTRACT FROM AUTHOR]

We study the convergence of the Prešić type k-step iterative method for a class of operators [ABSTRACT FROM AUTHOR]

Sedghi et al. (Mat. Vesn. 64(3):258-266, 2012) introduced the notion of a S-metric as a generalized metric in 3-tuples $S:X^{3} \rightarrow[0,\infty)$, where X is a nonempty set. The aim of this paper is to introduce the concept of an n-tuple metric $A: X^{n} \rightarrow[0,\infty)$ and to study its basic topological properties. We also prove some generalized coupled common fixed point theorems for mixed weakly monotone maps in partially ordered A-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of fixed points for set-valued mappings satisfying certain graph contractions with set-valued domain endowed with a graph. These results unify, generalize, and complement various known comparable results in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a class of multivalued mappings satisfying a Suzuki type generalized contractive condition in the framework of fuzzy metric spaces and to present fixed point results for such mappings. Some examples are presented to support the results proved herein. As an application, a common fixed point result for a hybrid pair of single and multivalued mappings is obtained. We show the existence and uniqueness of a common bounded solution of functional equations arising in dynamic programming. Our results generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present common fixed point results of quasi-weak commutative mappings on a closed ball in the framework of multiplicative metric spaces. Example is presented to support the result proved herein. We also study sufficient conditions for the existence of a common solution of multiplicative boundary value problem. Our results extend and improve various recent results in the existing literature. [ABSTRACT FROM AUTHOR]

Wardowski (2012) introduced a new type of contractive mapping and proved a fixed point result in complete metric spaces as a generalization of Banach contraction principle. In this paper, we introduce a notion of generalized F-contraction mappings which is used to prove a fixed point result for generalized nonexpansive mappings on star-shaped subsets of normed linear spaces. Some theorems on invariant approximations in normed linear spaces are also deduced. Our results extend, unify, and generalize comparable results in the literature. [ABSTRACT FROM AUTHOR]

We introduce two new types of fixed point theorems in the collection of multivalued and single-valued mappings in completemetric spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present fixed point results of multivalued mappings in the framework of partial metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. As an application of our main result, the existence and uniqueness of bounded solution of functional equations arising in dynamic programming are established. [ABSTRACT FROM AUTHOR]

In the framework of ordered G-metric spaces, fixed points of maps that satisfy the generalized (Ψ, ...)-Chatterjea type contractive conditions are obtained. The results presented in the paper generalize and extend several well known comparable results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a $$w^{*}$$ -compatible mappings to obtain coupled coincidence point and coupled common fixed points of nonlinear contractive mappings in partially ordered metric spaces. Our results generalize, extend, unify, enrich and complement various comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In [The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc, 136(2008), 1359-1373], Jachymski employed an interesting order theoretic approach to solve a fixed point problem in the setup of metric spaces endowed with a graph. On the other hand, in [Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728(1994), 183-197], Matthews introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, existence of a fixed point of generalized graphic contraction mappings in the framework of partial metric spaces is proved. An example is provided to validate our result. Results proved herein unify, generalize and complement various known comparable results in contemporary literature. [ABSTRACT FROM AUTHOR]

In [Numer. Funct. Anal. Optim. 32 (2011), 243-253], Azam, Fisher, and Khan introduced a notion of complex-valued metric spaces and obtained common fixed point results for mappings satisfying rational inequalities. In the present paper, employing the concept of asymptotically regular mappings, the existence of a fixed point is obtained in a complex-valued metric space. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, using the setting of generalized metric spaces, existence of unique common fixed point of two pairs of power contraction mappings satisfying (E.A)-property in generalized metric spaces is established. We also provide example to support the results presented herein. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain a Suzuki type fixed point theorem for a generalized multivalued mapping on a partial Hausdorff metric space. As a consequence of the presented results, we discuss the existence and uniqueness of the bounded solution of a functional equation arising in dynamic programming. [Copyright &y& Elsevier]

In this paper, we prove some coupled fixed point theorems for contractive mappings in partially ordered complete metric spaces under certain conditions to extend and complement the recent fixed point theorems according to Lakshmikantham and Ćirić [V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70(2009), 4341-4349] and Luong and Thuan [N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74(2011), 983-992]. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtained Suzuki type fixed point results for a generalized multi-valued mapping on a set equipped with two b-metrics. As a consequence, existence and uniqueness of solution of functional equation arising in dynamical programming is also derived. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the concept of a partial Hausdorff metric. We initiate study of fixed point theory for multi-valued mappings on partial metric space using the partial Hausdorff metric and prove an analogous to the well-known Nadlerʼs fixed point theorem. Moreover, we give a homotopy result as application of our main result. [Copyright &y& Elsevier]

Abstract: In this paper, using the setting of complete partially orderedG-metric spaces, some common fixed point results of maps that satisfy the generalized -weak contractive condition are obtained. [Copyright &y& Elsevier]

Using the setting of G- metric spaces, some new fixed point theorems for multivalued monotone mappings in ordered G- metric space X are proved, where the partial ordered ≤ in X is obtained by a pair of functions (Ψ, φ). [ABSTRACT FROM AUTHOR]

Abstract: In this paper, using the setting of generalized metric spaces, existence of unique common fixed point is established for mappings satisfying (E.A)-property under generalized strict contractive condition, as well as under some generalized contractions. Obtained results are proper extensions of the existing ones in metric space. We also provide example to support concepts and results presented herein. [Copyright &y& Elsevier]

We prove a coupled coincidence point theorem for a hybrid pair of single valued and multi-valued mappings satisfying generalized contractive conditions, defined on a partially ordered metric space. Our results unify, generalize and complement several known comparable results from the current literature. [ABSTRACT FROM AUTHOR]

Sufficient conditions for existence of random periodic points for random multivalued Econtractive operators in the frame work of separable metric spaces are obtained. These results are then used to obtain the random periodic point of ε- expansive random operators. [ABSTRACT FROM AUTHOR]

We prove some fixed point theorems for a T-Hardy-Rogers contraction in the setting of partially ordered partial metric spaces. We apply our results to study periodic point problems for such mappings. We also provide examples to illustrate the results presented herein. [ABSTRACT FROM AUTHOR]

Recently, Abbas et al. (2012) obtained some unique common fixed-point results for a pair of mappings satisfying (E.A) property under certain generalized strict contractive conditions in the framework of a generalized metric space. In this paper, we present common coincidence and common fixed points of two pairs of mappings when only one pair satisfies (E.A) property in the setup of generalized metric spaces. We present some examples to support our results. We also study well-posedness of common fixed-point problem. [ABSTRACT FROM AUTHOR]