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This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented. [ABSTRACT FROM AUTHOR]

Bipolar metric spaces and related fixed point theorems therein were introduced based on the motivation of measuring the distance between the elements of distinct sets. The question regarding the independence of these results from the analogous results on a fixed point of an induced mapping on a Cartesian product of two sets. We proved that bipolar metric space is metrizable and we presented two different approaches for defining a metric induced by a bipolar metric. Two obtained metric spaces demonstrated the lack of novelty of fixed point theorems for covariant and contravariant contraction. [ABSTRACT FROM AUTHOR]

Modular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular metric spaces. In particular, we examine the existence of interpolative Meir–Keeler contraction types via admissible mappings for fixed point theory. Our results bring together several results available in the current corresponding literature. [ABSTRACT FROM AUTHOR]

In this paper, the notion of hybrid Jaggi-Meir-Keeler type contraction is introduced. The existence of a fixed point for such operators is investigated. The derived results combine and extend a number of existing results in the corresponding literature. Examples are established to express the validity of the obtained results. [ABSTRACT FROM AUTHOR]

In this manuscript, p-cyclic orbital ɸ-contraction map over closed, nonempty, convex subsets of a uniformly convex Banach space X possesses a unique best proximity point if the auxiliary function ɸ is strictly increasing. The given result unifies and extend some existing results in the related literature. We provide an illustrative example to indicate the validity of the observed result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some common fixed point theorems for interpolative contraction operators using Perov operator which satisfy Suzuki type mappings. Further, some results are given. These results generalize several new results present in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a notion of the Górnicki-Proinov type contraction. Then, we prove the uniqueness and existence of the fixed point for such mappings in the framework of the complete metric spaces. Some illustrative examples are also expressed to strengthen the observed results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new sequential space as a generalization of M - metric spaces and Mb - metric spaces. In this generalized space we define two contractive mappings namely m - contraction and m - quasi-contraction and prove some fixed point theorems for such type of mappings. Several illustrative examples have been presented in strengthening the hypothesis of our theorems. [ABSTRACT FROM AUTHOR]

In this article, we propose a generalization of both b -metric and dislocated metric, namely, dislocated extended b -metric space. After getting some fixed point results, we suggest a relatively simple solution for a Volterra integral equation by using the technique of fixed point in the setting of dislocated extended b -metric space. [ABSTRACT FROM AUTHOR]

Very recently, the notion of extended b-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended b-metric space is given. [ABSTRACT FROM AUTHOR]

Kada, Suzuki, and Takahashi introduced and studies the concept of ω- distance in fixed point theory. In this paper, we generalize and unify Ćirić' and Fisher fixed points results for quasi-contractions on metric space to ω-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in metric spaces. [ABSTRACT FROM AUTHOR]

We prove a fixed point theorem for function spaces, that is a very efficient and convenient tool for the investigations of various operator inequalities connected to Ulam stability issues, in classes of functions taking values in various spaces (e.g., in ultrametric spaces, dq-metric spaces, quasi-Banach spaces, and p -Banach spaces). The theorem is a natural generalization and extension of the classical Banach Contraction Principle and some other more recent results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present existence and uniqueness results for the solution of a system of operator inclusions. Data dependence, well-posedness, Ulam-Hyers stability, and Ostrovski stability of the coupled fixed point system are studied. The basic idea is to apply a fixed point theorem for an appropriate operator on the Cartesian product of a given b- metric space endowed with a graph. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of α-ψ-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle. [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]

In this paper, by using the measure of noncompactness and Meir-Keeler type mappings, we prove some new fixed point theorems for some certain mappings, namely, the weaker ϕ-Meir-Keeler type contractions, asymptotic weaker ϕ-Meir-Keeler type contractions, asymptotic sequence {øi}-Meir-Keeler type contraction, ξ-generalized comparison type contraction, and R-functional type ψ-contractions. Our results improve and hence cover the well-known Darbo's fixed point theorem, and several related recent fixed point results. [ABSTRACT FROM AUTHOR]

We provide sufficient conditions under which the set of common fixed points of two self-mappings f, g : X → X is nonempty, and every common fixed point of f and g is the zero of a given function ϕ : X → [0,∞). Next, we show the usefulness of our obtained result in partial metric fixed point theory. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new contractive condition. We prove the existence and uniqueness of a fixed point of self-mapping under this new contractive condition. Moreover, we observe analog of these results for the mappings that satisfy the property P. An application on integral equations is presented to illustrate the main result. Our results extend and generalize well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of fixed points for a new class of contractive mappings involving rational expressions, which enable us to extend many known results in the literature. We consider illustrative example and consequences to underline the novelty of the main results. [ABSTRACT FROM AUTHOR]

We consider some extension of MKC mappings in the framework of complete dislocated metric spaces. Besides the theoretical results, we also consider some illustrative examples. Further, we state and prove that our main results improved the related results in the frame of generalized Ulam-Hyers stability theory. [ABSTRACT FROM AUTHOR]

We introduce the notion of quasi-JS-metric space. After defining the basic topological properties of quasi-JS-metric space, we investigate fixed point of certain mapping in the frame of complete quasi-JS-metric space. Our results unify and cover several existing fixed point theorems in distinct structures (such as standard quasi-metric spaces, quasi-b-metric spaces, dislocated quasi-metric spaces, and quasi-modular spaces) in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to generalize fixed point theorems introduced by Jleli et al. (J. Inequal. Appl. 2014:38, ) by using the concept of triangular α-orbital admissible mappings established in Popescu (Fixed Point Theory Appl. 2014:190, ). Some examples are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of a fixed point of certain operators in the setting of complete quasi- b-metric-like spaces via admissible mappings. Our results improve, extend, and unify several well-known existence results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the sufficient condition for the existence of best proximity points for non-self-multivalued mappings. Additionally, we discuss the stability theorem for such mappings. Our results improve and generalize some existing results on the topic in the literature, in particular, the results of Lim and of Abkar and Gabeleh. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces. [ABSTRACT FROM AUTHOR]

The main aim of this short-note is point out that certain hypotheses assumed on some results in the very recent paper (Yang in J. Inequal. Appl. 2014:275, 2014) are unnecessary, and the results contained in that manuscript can easily be improved. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the fixed point results in the context of complex-valued metric spaces can be obtained as a consequence of corresponding existing results in the literature in the setting of associative metric spaces. In particular, we deduce that any complex metric space is a special case of cone metric spaces with a normal cone. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a conditionally F-contraction in the setting of complete metric-like spaces and we investigate the existence of fixed points of such mappings. Our results unify, extend, and improve several results in the literature. [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, 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 article we review the notion of random coupled coincidence and prove a random coupled fixed point theorem under a certain set of conditions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the non-cooperative equilibrium problem of two person games in the setting of game theory and propose a solution via coupled fixed point results in the context of partial metric spaces. We also realize that our coupled fixed point results can be applied to get a solution of a class of nonlinear Fredholm type integral equations. [ABSTRACT FROM AUTHOR]

We show that a quasi-metric space is right K-sequentially complete if and only if it satisfies the property of the weak form of Ekeland's Variational Principle. This result solves a question raised by S. Cobzaş (2011) [3] . [ABSTRACT FROM AUTHOR]

We introduce the notion of generalized F-Suzuki type contraction in b-metric spaces and investigate the existence of fixed points of such mappings. The presented results generalize and improve several results of the topics in the literature. [ABSTRACT FROM AUTHOR]

We show that the main result in the work by Mutlu et al. is not true. We explain point by point some of its main mistakes and we propose an alternative version to smooth away the defects of it. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new class of contractive mappings such as fuzzy α-ψ-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results. [ABSTRACT FROM AUTHOR]

Very recently, the notion of a Ψ-Geraghty type contraction was defined by Gordji et al. (Fixed Point Theory and Applications 2012:74, 2012). In this short note, we realize that the main result via Ψ-Geraghty type contraction is equivalent to an existing related result in the literature. Consequently, all results inspired by the paper of Gordji et al. in (Fixed Point Theory and Applications 2012:74, 2012) can be derived in the same way. [ABSTRACT FROM AUTHOR]

We introduce the notions of (α - ϕ - ψ)-weaker Meir-Keeler contractive mappings and (α - φ)-stronger Meir-Keeler contractive mappings. We discuss the existence of periodic points in the setting of generalized quasi-metric spaces. Our results improve, extend, and generalize several results in the literature. [ABSTRACT FROM AUTHOR]

We consider the existence of a fixed point of (α - ψ) -contractive mappings in the context of generalized quasimetric spaces without Hausdorff assumption. The obtained results extend several results on the topic in the literature. [ABSTRACT FROM AUTHOR]

In the very recent paper of Akbar and Gabeleh (2013), by using the notion of P-property, it was proved that some late results about the existence and uniqueness of best proximity points can be obtained from the versions of associated existing results in the fixed point theory. Along the same line, in this paper, we prove that these results can be obtained under a weaker condition, namely, weak P-property. [ABSTRACT FROM AUTHOR]

We extend the notion of (αψ, βφ)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts. [ABSTRACT FROM AUTHOR]

We admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014)] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Đoric and Lazović (2011)] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (α, r)-admissible contractions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of expansive mappings called generalized (ξ, α)-expansive mappings and investigate the existence of a fixed point for the mappings in this class. We conclude that several fixed-point theorems can be considered as a consequence of main results. Moreover, some examples are given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

We introduce the notion of generalized weaker (α-ø-φ)-contractive mappings in the context of generalized metric space. We investigate the existence and uniqueness of fixed point of such mappings. Some consequences on existing fixed point theorems are also derived. The presented results generalize, unify, and improve several results in the literature. [ABSTRACT FROM AUTHOR]

We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. [ABSTRACT FROM AUTHOR]

A class of α-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

Very recently, Ahmed et al. introduced the notion of quaternion-valued metric as a generalization of metric and proved a common fixed point theorem in the context of quaternion-valued metric space. In this paper, we will show that the quaternion-valued metric spaces are subspaces of cone metric spaces. Consequently, the fixed point results in such spaces can be derived as a consequence of the corresponding existing fixed point result in the setting cone metric spaces. [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]

Very recently, a notion of cone b-metric was introduced as a generalization of b-metric, and some related fixed point results were obtained. In this paper, we investigate the answer to the question whether the given results generalize the existing ones or are equivalent to them. MSC: 46N40, 47H10, 54H25, 46T99. [ABSTRACT FROM AUTHOR]