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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 focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [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 study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

The paper is devoted to prove the existence of solutions for an infinite system of non- linear integral equations. This system is investigated in the WC-Banach algebra C(I; c0), the space of all continuous functions acting from an interval I into the sequence space c0. Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operat- ors acting onWC-Banach algebra involving w-contractive operators. [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 aim of this paper is to propose a new faster iterative method, called the MNiteration process, for approximating a fixed point of continuous functions on an arbitrary interval. Then, a necessary and sufficient condition for the convergence of the MN-iteration of continuous functions on an arbitrary interval is established. We also compare the rate of convergence between the proposed iteration and some other iteration processes in the literature. Specifically, our main result shows that MN-iteration converges faster than NSP-iteration to the fixed point. We finally give numerical examples to compare the result with Mann, Ishikawa, Noor, SP and NSP iterations. Our findings improve corresponding results in the contemporary literature. [ABSTRACT FROM AUTHOR]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of nonlinear Liouville–Caputo fractional differential equations equipped with a new set of nonlocal boundary conditions involving an arbitrary strip together with two sets of nonlocal multi-points on either part of the strip on the given domain. We emphasize that the boundary conditions considered in this study are formulated with respect to the sum and difference of the unknown functions. We apply the well-known tools of the fixed point theory to derive the main results. Examples are presented for the illustration of the obtained results. [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, a two dimensional discrete-time predator-prey system with weak Allee effect, affecting the prey population, is considered. The existence of the positive fixed points of the system and topological classification of coexistence positive fixed point are examined. By using the bifurcation theory, it is shown that the discrete-time predator-prey system with Allee effect undergoes flip and Neimark-Sacker bifurcations depending on the parameter a. The parametric conditions for existence and direction of bifurcations are investigated. Numerical simulations including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the system are performed to validate analytical results. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the considered system. Finally, the OGY feedback control method is implemented to stabilize chaos existing in the system. [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]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [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 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, by considering theWardowski's technique, we present fixed point results for multivalued mapping on a space with two metrics. Also, taking into account β-admissibility of a multivalued mapping, we provide some more general 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]

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]

In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings. For this scheme, we prove some convergence theorems in CAT(0) spaces. In process, we remove a restricted condition (also called end-point condition) in previous several existing results. Thus, several relevant results cited in the literature generalize and improve. [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]

In this paper, we introduce the concept of a pair (f, h) called upper class of type II and αβ-contractive mappings. We obtain that all the corresponding established results of Hussain et al. [7] are immediately consequences of our main result. Our main result generalizes and modifies several existing results in literature. Also, an example is given to support the main result. [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]

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 give a new proof of a result by S. Reich and A.J. Zaslavski (S. Reich and A.J. Zaslavski, A fixed point theorem for Matkowski contractions, Fixed Point Theory, 8(2007), No. 2, 303-307). Some new fixed point theorems for nonself generalized contractions are also given. [ABSTRACT FROM AUTHOR]

In this paper we will prove a fixed point theorem of Perov type for cyclic contractions on complete generalized metric spaces. Then, as an application, we will study the existence, uniqueness and approximation of the solution for a system of integral equations. [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]

This paper is concerned with the existence of solutions for initial value problems of functional and neutral functional Hadamard type fractional differential inclusions. We apply appropriate fixed point theorems for multivalued maps to obtain the existence results for the given problems covering convex as well as non-convex cases. Some illustrative examples are also presented. [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]

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]

Let us consider a non-self mapping T : A → B, where A and B are two nonempty subsets of a metric space (X,d). The aim of this paper is to solve the nonlinear programming problem that consists in minimizing the real valued function x → d(x,T x), where T belongs to a new class of non-self mappings. In especial case, existence and uniqueness of fixed point for Kannan type self mappings are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, the convergence of Mann iterative process with errors for generalized Lipschitz ϕ-quasi-accretive operators is proved in uniformly smooth Banach spaces. Our results improve the corresponding results of Chidume et al.[2]. [ABSTRACT FROM AUTHOR]

In this paper, we prove some properties of quasi-metric spaces and state some fixed point theorems in this setting. As applications, we show that most of recent results on G-metric spaces in [3, 10] may be also implied from certain fixed point theorems on metric spaces and quasi-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the class of generalized nonexpansive mappings in Banach spaces. This class contains both the classes of nonexpansive and α-nonexpansive mappings. In addition, we obtain some fixed point and coincidence point theorems for generalized nonexpansive mappings in uniformly convex Banach spaces. Our results extend some wellknown results in literature. [ABSTRACT FROM AUTHOR]

This paper investigates the existence of solutions for a sequential fractional differential equation of arbitrary order ξ + 1; ξ ∊ (n-1, n), n ⩾ 2 with three-point nonlocal boundary conditions. We make use of standard tools of fixed point theory to establish our existence results. An illustrative example and some special cases are also discussed. [ABSTRACT FROM AUTHOR]

This paper is mainly concerned with existence of mild solutions for a first order impulsive neutral fractional integrodifferential inclusions with nonlocal initial conditions in α- norm. We assume that the linear part generates an analytic semigroup and transform it into an integral inclusion. By using a fixed point theorem for multi-valued maps due to Dhage, a main existence theorem is established. Finally, we present an example to illustrate this main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we present a fixed point theorem for a new type of contractive mappings. Our main result extends and unifies some well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we use the order relation on partial metric spaces defined by [1] to prove some new fixed point theorems for multivalued monotone mappings in ordered partial metric spaces. [ABSTRACT FROM AUTHOR]

In this paper we present a new acceleration method for accelerating some numerical sequences of successive approximations that arises in solving certain nonlinear equations. We give a convergence result and some numerical examples to illustrate the abilities of the proposed new acceleration technique. [ABSTRACT FROM AUTHOR]

In the present paper, we give a common fixed point theorem for two weakly increasing mappings on ordered Hausdorff uniform spaces, using the distance p: Two multivalued versions of this result are also presented. [ABSTRACT FROM AUTHOR]

In this paper we prove existence results for boundary value problems for higher-order differential inclusion x(n) (t) ϵ F(t, x (t)) with nonlocal boundary conditions, where F is a compact convex L¹-Carathéodory multifunction. [ABSTRACT FROM AUTHOR]