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This paper introduces self maps satisfying (CLRα) and (CLRαβ) property in Modified Intuitionistic Fuzzy Soft Metric Space (MIFSMS). Moreover, we have also extended common fixed point theorems for weakly compatible maps satisfying common limit range property in the setting of MIFSMS. We have also given an application utilising our new results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912-3919, 2011]. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some existence results for multivalued contraction mappings in the context of an O-complete orthogonal metric space (not necessarily complete metric space). Also, we provide a partial solution to Reich’s problem for multivalued orthogonal contraction mappings and extend Mizoguchi-Takahashi’s point theorem. In addition, we give an example to demonstrate the applicability of our established results. We study the solution of a differential equation and its Ulam’s stability as an application of the obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a system of N -fixed point equations in metric spaces. The existence and uniqueness of solution and an iterative algorithm for approximating the solution are studied. This system of N -fixed point equations is an extension of the classical of fixed point equation x = T x. The results of this paper improve several important works recently published in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we extend the result of Romaguera [21] with the aid of best proximity point theory on partial metric spaces by considering the approach of Haghi et al. [9], and so celebrated Boyd-Wong fixed point theorem [7]. We first introduce two concepts called generalized proximal BW-contraction and generalized best BW-contraction. Then, we obtain some best proximity point theorems for such mappings. To illustrate the effectiveness of our results, we provide some nontrivial and interesting examples. Finally, unlike homotopy applications existing in the literature, we present for the first time an application of the best proximity result to the homotopy theory. [ABSTRACT FROM AUTHOR]

In the paper, we will discus some τ-topological properties of the set F (S0,T,H) := {x ∈ X : S0x ∈ Tx+Hx}, where T is multivalued operator, S0 and H are two single valued operators acting on a Hausdorff locally convex space X and τ is a weaker Hausdorff locally convex topology on X. Moreover, when X is a τ-angelic space with the so-called τ-Krein-Šmulian property, we will provide some new variants of fixed point theorems for multivalued operators. Our results are formulated in terms of τ-upper semicontinuity, τ-S0-demicom-pactness and families of axiomatic measures of noncompactenss. [ABSTRACT FROM AUTHOR]

In this paper, we prove two new general fixed point theorems in rectangular b-metric spaces. As applications, we answer two open questions in rectangular b-metric spaces posed. [ABSTRACT FROM AUTHOR]

In this paper, we establish some Ostrowski type integral inequalities for functions of two variables involving generalized fractional integrals. The results presented here provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

In this paper, we will prove some fixed point results using a Pompeiu type metric on Pcl(X), for multi-valued operators satisfying two conditions: contractivity and monotonicity. The approach is based on a fixed point theorem for a multi-valued operator in the setting of a b-metric space. Several qualitative properties(well-posedness, Ulam-Hyers stability) are also obtained. In the second part of this paper, we will consider the extended coupled fixed point problem for a multi-valued operator. We will consider the problem of the existence of the solutions. Data dependence and well-posedness of the extended coupled fixed point problem are also discussed. [ABSTRACT FROM AUTHOR]

In this paper we find all involutive solutions X ∈ Cn×n of the Yang-Baxter matrix equation AXA = XAX, where A ∈ Cn×n is a given involutory matrix. The construction is algorithmic. It is based on the concept of quadratic matrices. Algorithms for generating concrete involutive solutions of the Yang-Baxter matrix equation AXA = XAX are also presented along with several examples. [ABSTRACT FROM AUTHOR]

In this paper, we examine a generalized convexity type inequality, called e-convexity. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of a non-trivial solution in W 1,p(x) 0 (Ω) for the problem ( ∆p(x)u = f(x,u,∇u) in Ω, u = 0 in Ω. The proof is based on Schaefer's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we extend the relation-theoretic contraction principle due to Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702) for Matkowski contractions employing a locally T-transitive binary relation. Our results improve and enrich several fixed point theorems of the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, first we prove a common fixed point theorem for pairs of weakly compatible mappings satisfying a generalized -weak contraction condition that involves cubic terms of metric functions. Secondly, we prove some results using different variants of R-weakly commuting mappings. At the end, we give an application in support of our results. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we introduce the concept of a complex valued fuzzy b-metric space, which is inspired by the work of Shukla et al. [24]. Also, we investigate some of its topological properties which strengthen this concept. Next, we establish some fixed point theorems in the context of complex valued fuzzy b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature. Moreover, we provide some applications on the existence and uniqueness of solutions for a certain type of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

In this paper, a general fixed point theorem for quasi-contractions in b-metric spaces, which is a sharp improvement of Amini-Harandi's result, Mitrovic and Hussain's result, and is a generalization of many b-metric fixed point theorems in the literature, is proved. The technique overcomes some limits in b-metric fixed point theory compared to metric fixed point theory. The obtained results are also supported by examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some a Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper we generalize the well-known class of quasi contractions pairs, by using the so-called Geraghty's property and by controlling the contractive inequality with an altering distance function. For this class, in the setting of b-metric spaces, we prove the existence and uniqueness a of common fixed point assuming some non commutative notions. Finally, for this class of mappings we prove the b-convergence of the Jungck-Mann iterative scheme under suitable conditions on the b-metric space and on the altering distance function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of an admissible extended Z-contraction mapping in the setting of extended b-metric spaces. As an application, we consider Ulam stability problems based on our contractions. The presented results cover several existing results in the literature. [ABSTRACT FROM AUTHOR]

It is well known that for any nonempty closed convex subset C of a Hilbert space, any best approximation y ∈ C of the point x satisfies the inequality ||x-y||² + ||z-y||² ≤ ||x-z||² for all Z ∈ C. In this paper, we first introduce and study a new subset of best approximations involving this inequality in general metric spaces. Then, we provide some equivalent conditions which characterize Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

Two common fixed point theorems for a class of contractive mappings are proved in metric spaces. As an application, the existence and uniqueness of solution for a functional equation arising in dynamic programming is given. The results presented in this paper generalize some known results in the literature. [ABSTRACT FROM AUTHOR]

Recently, B. Samet et al. (Fixed Point Theory and Appl. 2013:5, 2013, doi:10.1186/1687-1812-2013-5) has introduced the concept of new contraction mappings and obtained results on the fixed point for nonlinear contractive mappings in a metric space. In the present paper, we introduce the concept of a new contraction via the measure of non-compactness on a Banach space, we obtain a few generalizations of Darbo fixed point theorem and extend some recent results of Aghajani et al. We also show the applicability of obtained results to the theory of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the concept of partially ordered rectangular metric spaces using the notation (X,≤d). Also, we give a generalized contractive condition in the context of partially ordered rectangular metric space for all comparable pair of X. Our results extend and generalize the well-known results of [13], [1], [14] and [11]. [ABSTRACT FROM AUTHOR]

In this paper, an effort has been made to improve the notion of α-Geraghty contraction type mappings and establish some common fixed point theorems for a pair of α-admissible mappings under the improved approach of generalized rational α-Geraghty contractive type condition in a complete metric space. An example has been constructed to demonstrate the novelty of these results. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of contraction: the almost local contractions. Then, we prove the existence and uniqueness of a fixed-point for local almost contractions in two cases: with constant and variable coefficients of contraction. [ABSTRACT FROM AUTHOR]

In this paper a compactness criterion in weighted variable Lebesgue spaces is proved. In particular, are proved a compactness criterion in variable exponent sequence Lebesgue spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to transpose some of the results regarding the coupled fixed point theory, developed by Bhaskar and Lakshmikantham [7], using the approaches of Ben-El-Mechaiekh [2], Asgari, Mousavi [1] and Berinde [3]. The first approach replaces the partial order relation from the Ran-Reurings fixed point theorem [10] with a transitive one, the second one uses a reflexive-only relation and whereas the third one introduces the tripled fixed points. Our aim is to obtain some generalized fixed point theorems, containing a more simple symmetrical condition, also extending them for the case of tripled fixed point. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove common fixed point theorems for two operators without the assumption of continuity on a set endowed with vector-valued b-metric and we also study the case of two vector-valued b-metrics. The well-posedness of the fixed point problem is also discussed and an application is presented for systems of operator equations in complete b-normed vector space. Our results improve and generalize theorems 2 and 5 of M. Boriceanu [5]. [ABSTRACT FROM AUTHOR]

In this paper, we will consider the coupled fixed point problem for single-valued operators satisfying a symmetric contraction condition with respect to maximum. An application to a periodic boundary value problem illustrates the results. The study of a coupled coincidence problem is also suggested. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized weakly α-contractive mappings and give some common fixed point results for this type of contraction. The presented theorems extend, generalize and improve many existing results in the literature. Two examples as well as an application to ordinary differential equations are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we have given a criteria for the existence of common fixed point for pair of mappings in 2-metric spaces and establish common fixed point theorems for certain class of contractive type mappings. The results presented here, generalize some well known fixed point theorems given in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we obtained some fixed point results for continuous mappings satisfying a generalized contractive condition in the setting of two metrics space endowed with a binary relation. Our theorems generalize and extend several known results in the literature. As application, we establish an existence theorem for the solution of a nonlinear first order differential equation. [ABSTRACT FROM AUTHOR]

Let W = {w1;w2; … ;wk} be an ordered set of vertices of G and let v be a vertex of G. The representation r(v|W) of v with respect to W is the k-tuple (d(v,w1),d(v,w2), … ; d(v,wk)). W is called a resolving set or a locating set if every vertex of G is uniquely identified by its distances from the vertices of W, or equivalently, if distinct vertices of G have distinct representations with respect to W . A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension of G, denoted by dim(G). Metric dimension is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). In this paper, we study the metric dimension of barycentric subdivision of Cayley graphs Cay(Zn ⊕Zm). We prove that these subdivisions of Cayley graphs have constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of Cayley graphs Cay(Zn⊕Zm). [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results using mixed weakly monotone property and altering distance function in the setting of S-metric space. Our result generalizes the result of Lakshmikantham and Ciric [V. Lakshmikantham and L. Ciric, Coupled common fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, 70, (2009), 4341 - 4349]. [ABSTRACT FROM AUTHOR]

In this paper we show that on complete metric spaces the class of weakly Picard operators contains some operators which are more general than the class of almost contractions. [ABSTRACT FROM AUTHOR]

In this paper, we use the order relation on uniform spaces defined by [5] to introduce the notion of compatibility of mappings in an ordered uniform space and use this notion to establish coupled coincidence point theorems to ordered uniform space. An example is also given. [ABSTRACT FROM AUTHOR]

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of contractions of Berinde-Suzuki type on a partial metric space. Moreover, using our results, as application we obtain a new characterization of partial metric 0-completeness. Finally, we give a typical application of fixed point methods to integral equation, by using our results. [ABSTRACT FROM AUTHOR]