Search

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 notion of occasionally weakly compatible mappings, and Semi compatible mappings in fuzzy metric space is discussed in this research. The paper investigates the Common fixed-point theorems in fuzzy metric spaces. By taking the property of commutativity of pair mappings, the pairwise semi-compatible mappings and occasionally weakly compatible mappings, satisfying constructive type condition for six self-mappings the common fixed-point theorems in fuzzy metric spaces were proved. The result improves and generalizes other similar results in the literature. [ABSTRACT FROM AUTHOR]

In this paper we give some fixed point theorems for nonself generalized contractions on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. S¸erban (I.A. Rus, M.-A. S¸erban, Some fixed point theorems for nonself generalized contractions, Miskolc Math. Notes, 17(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A.J. Zaslavski, A note on Rakotch contractions, Fixed Point Theory, 9(2008), no.1, 267-273) in complete metric spaces. We prove our results without using the completeness of the metric structure. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of F--G--contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F--metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of the fixed points of set-valued contractions on ordered g-metric spaces. The first part of the paper deals with the existence of fixed points for these mappings where the contraction condition is assumed for comparable variables. A coupled fixed point theorem is also established in the second part. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of dislocated Sb-metric space and describe some fixed point theorems concerning F-contraction in the setup of such spaces. We provide some examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we, motivated by Mihet [2], give the concept of two nonlinear contractions ((φ, ε-λ)-contraction and (f, bn)-contraction) in KM-fuzzy metric spaces, and obtained some fixed point theorems. We answer the open question posed by Mihet in [2, open question 2]. Finally, an example can be used to be exemplify our results. [ABSTRACT FROM AUTHOR]

In this paper, we develop some fixed point theorems by using auxiliary functions for maps satisfying a rational type contractive condition in partially ordered S-metric spaces. Conditions for uniqueness of fixed point are also discussed. Our results generalize some existing results in the literature of S-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove a fixed point theorem for a system of maps on the finite product of metric spaces. Our result generalizes the result of Matkowski (Bull Acad Pol Sci Sér Sci Math Astron Phys 21:323-324, 1973), Cosentino and Vetro (Filomat 28(4):715-722, 2014) and Hardy and Rogers (Can Math Bull 16(2):201-206, 1973) and other results in the literature. Moreover, we have an application for a system of functional equations and an example to illustrate our result. [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]

In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we consider an iterative procedure for approximating common fixed points of two generalized asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.This will extend the results of Cholamjiak and Suantai, Khan and those generalized therein to the case of generalized asymptotically quasi-nonexpansive mappings and by a faster iterative procedure. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects. [ABSTRACT FROM AUTHOR]

Let f be an holomorphic function which maps the unit disk into itself. In this paper, consider the zero of order k ( i.e., $f(z)-f(0)$ (or $f(z)$ ) has a zero of order k at $z=0$ ), we obtain the sharp estimates of the classical boundary Schwarz lemma involving the boundary fixed point. The results presented here would generalize the corresponding result obtained by Frolova et al. (Complex Anal. Oper. Theory 8:1129-1149, 2004). [ABSTRACT FROM AUTHOR]

In this paper, we present an Ekeland type variational principle, Takahashi type minimization theorem, Caristi type fixed point theorem and a generalized Oettli-Thera's equivalent form on complete D-metric space. We also prove that they are equivalent. The results present in this paper unify, improve and extend many known results due to Zhong, Ekeland, Takahashi, Caristi, and others. [ABSTRACT FROM AUTHOR]

Abstract: The concept of weak contraction from the case of single-valued mappings is extended to multi-valued mappings and then corresponding convergence theorems for the Picard iteration associated to a multi-valued weak contraction are obtained. The main results in this paper extend, improve and unify a multitude of classical results in the fixed point theory of single and multi-valued contractive mappings and also improve recent results from the paper [P.Z. Daffer, H. Kaneko, Fixed points of generalized contractive multi-valued mappings, J. Math. Anal. Appl. 192 (1995), 655–666]. [Copyright &y& Elsevier]

In the present paper, we give a new approach to Caristi's fixed point theorem on non-Archimedean fuzzy metric spaces. For this we define an ordinary metric d using the non-Archimedean fuzzy metric M on a nonempty set X and we establish some relationship between (X, d) and (X, M, *). Hence, we prove our result by considering the original Caristi's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper we prove a common fixed point theorem in fuzzy 2- metric space on six self-mappings using the concept of compatible of type (K) and Property (E.A.). [ABSTRACT FROM AUTHOR]

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F : (0 , + ∞) → (− ∞ , + ∞) . According to the recently obtained results, this was possible (Wardowski's method) only if two more properties (F 2) and (F 3) were used instead of the aforementioned strictly increasing (F 1) . Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that α (u , v) = 1 for every u and v from metric space Ξ , we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained. [ABSTRACT FROM AUTHOR]

In this paper, we apply the concept of cyclic (φ)-contraction for presenting a fixed point theorem on Hausdorff uniform space. Some more general results are also obtained in Hausdorff uniform space. [ABSTRACT FROM AUTHOR]

In this paper a general fixed point theorem for a pair of mappings satisfying an implicit relation is proved. This theorem generalizes and improves Theorem 2.1 [19], removing the assumption of weak reciprocally continuity, relaxing the compatibility R-weakly commutativity of type (Af) or (Ag) to weak continuity and replacing the completeness of the space with completeness of a subspace. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we show that fixed point generalizations to partial metric spaces can be obtained from the corresponding results in metric spaces. We consider some cases to demonstrate this fact. [Copyright &y& Elsevier]

We consider the inhomogeneous version of the fixed-point equation of the smoothing transformation, that is, the equation , where means equality in distribution, is a given sequence of non-negative random variables and is a sequence of i.i.d. copies of the non-negative random variable X independent of . In this situation, X (or, more precisely, the distribution of X) is said to be a fixed point of the (inhomogeneous) smoothing transform. In the present paper, we give a necessary and sufficient condition for the existence of a fixed point. Furthermore, we establish an explicit one-to-one correspondence with the solutions to the corresponding homogeneous equation with C = 0. Using this correspondence and the known theory on the homogeneous equation, we present a full characterization of the set of fixed points under mild assumptions. [ABSTRACT FROM AUTHOR]

This paper is aimed at proving the existence of a solution to the Volterra-Hamerstain integral equations in partially-ordered spaces. To this end, some fixed point theorems are proved in this kind of spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present some fixed point theorems in a partially ordered complete metric space . The usual Caristi’s condition that for each is weakened at the expense that the mapping is nondecreasing with respect to a partial order. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to prove a strong convergence theorem for a pair of sequences of nonexpansive mappings in a Hilbert space, where one of them is a strongly nonexpansive sequence, and provide some applications of the theorem. [Copyright &y& Elsevier]

Recently, Azam, Arshad and Beg [4] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is to show the existence of coincidence and fixed points for mappings satisfying property (E.A) in cone metric spaces. Also, we give periodic point theorems in cone metric spaces. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we discuss the following -Laplacian -point boundary value problem on time scales : where for . Some new existence criteria for at least three positive solutions are established by using a generalization of the Leggett-Williams fixed point theorem due to Bai and Ge. An example is also given to demonstrate the main result. [Copyright &y& Elsevier]

Abstract: Recently, D. Ilić and V. Rakočević [D. Ilić, V. Rakočević, Quasi-contraction on a cone metric space, Appl. Math. Lett. (2008) doi:10.1016/j.aml.2008.08.011] proved a fixed point theorem for quasi-contractive mappings in cone metric spaces when the underlying cone is normal. The aim of this paper is to prove this and some related results without using the normality condition. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the boundary value problem on the half-line where and are continuous. We show the existence of positive solutions by using a fixed point theorem in cones. [Copyright &y& Elsevier]

On a vector space, one can define an order by using a cone in the vector space. In this way, Huang and Zhang reviewed cone metric spaces as a generalization of metric spaces with a different view (J. Math. Anal. Appl. 2007; 332:1468-1476). Most known cones are normal with normal constant M = 1. In this paper, we shall give some results about fixed point of multifunctions on the cone metric spaces with normal constant M = 1. In this way, we shall provide a generalization for main results of Kunze et al. (J. Math. Anal. Appl. 2007; 330:159-173). [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider two types of second-order neutral functional differential equations with infinite distributed delay. By choosing available operators and applying Krasnoselskii’s fixed-point theorem, we obtain sufficient conditions for the existence of periodic solutions to such equations. [Copyright &y& Elsevier]

Abstract: This paper is mainly concerned with the existence of solutions for a certain class of fractional differential inclusions with boundary conditions. By using Bohnenblust–Karlin’s fixed point theorem, a main existence theorem is obtained. As an application of this main theorem, we establish two existence results when the multi-valued nonlinearity has sub-linear or linear growth in the state variable . Our results are even new when applied to a corresponding single-valued problem. [Copyright &y& Elsevier]

In this paper we study the existence of coincidences and fixed points of generalized hybrid contractions involving single-valued and multivalued maps in generalized metric spaces. Some special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered. [ABSTRACT FROM AUTHOR]

In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established. [ABSTRACT FROM AUTHOR]

By applying the well known Leggett–Williams multiple fixed point theorem and fixed point theorem of cone expansion and compression, this paper investigates the existence of multiple positive solutions of periodic boundary value problems for first order differential equations. Meanwhile, two examples are worked out to demonstrate the main results. [Copyright &y& Elsevier]

We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we shall give some existence results for a certain class of first order impulsive dynamic equations on time scales with nonlocal initial conditions. The approach used is the Sadoviskii’s fixed point theorem. [Copyright &y& Elsevier]

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991). [ABSTRACT FROM AUTHOR]

This paper is concerned with the following systemΔ3u1(k)+f1(k,u1(k),u2(k))=0,k∈[0,T],Δ3u2(k)+f2(k,u1(k),u2(k))=0,k∈[0,T],with the Dirichlet boundary conditionu1(0)=u1(1)=u1(T+3)=0=u2(0)=u2(1)=u2(T+3).By using Leggett–Williams fixed point theorem, sufficient conditions are obtained for the existence of three positive solutions to the above system. [Copyright &y& Elsevier]

In this paper, necessary and sufficient conditions for the existence and classification of positive solutions of the higher order neutral differential equationr(t)x(t)−∑i=1mPi(t)x(t−τi)(n−1)′+ft,x(t−σ1),…,x(t−σl)=0are obtained, where Pi(t)⩾0, i=1,…,m, f(t,μ1,…,μl)∈C([t0,∞)×Rl,R). [Copyright &y& Elsevier]

In this paper, we consider the following dynamical system on a measure chain: u1ΔΔ(t)+f1(t,u1(σ(t)),u2(σ(t)))=0, t∈[a,b],u2ΔΔ(t)+f2(t,u1(σ(t)),u2(σ(t)))=0, t∈[a,b],with the Sturm–Liouville boundary value conditionsαui(a)−βuiΔ(a)=0, γui(σ(b))+δuiΔ(σ(b))=0 for i=1,2.Some results are obtained for the existence of three positive solutions of the above problem by using Leggett–Williams fixed point theorem. [Copyright &y& Elsevier]

This paper is devoted to a nonlinear averaging principle for periodic solutions of a class of second order inclusions. In addition an existence theorem for periodic solutions of such inclusions is established. This work which complements the abstract nonlinear averaging principle worked out in Couchouron and Kamenski (Nonlin. Anal. 42 (2000) 1101) makes a synthesis of the methods contained in Couchouron and Kamenski and Couchouron and Precup (Electron. J. Differential, Equations 4 (2002) 1) and represents a (nonvariational) topological approach for boundary values problems. [Copyright &y& Elsevier]

In this paper we present two new results for the existence of fixed points of multivalued mappings with closed values on quasi metric space. First we introduce the multivalued Fd-contraction on quasi metric space (X; d) and give a fixed point result related to this concept. Then taking into account the Q-function on a quasi metric space, we establish a Q-function version of this concept as multivalued Fq-contraction and hence we present a fixed point result to see the effect of Q-function to existence of fixed point of multivalued mappings on quasi metric space. [ABSTRACT FROM AUTHOR]

This paper deals with the first-order delayed differential systems {u′+a(t)u=h(t)v+f(t,u(t−τ(t))),v′+b(t)v=g(t,u(t−τ(t))), where a, b, τ, h are continuous ω-periodic functions with ∫0ωa(t)dt=0 and ∫0ωb(t)dt>0; f∈C(R×[0,∞),R) and g∈C(R×[0,∞),[0,∞)) are ω-periodic with respect to t. By means of the fixed point theorem in cones, several new existence theorems on positive periodic solutions are established. Our main results enrich and complement those available in the literature. [ABSTRACT FROM AUTHOR]