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Abstract: In this paper, we study a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of variational inequalities for two inverse strongly accretive mappings and the set of common fixed points of an infinite family of nonexpansive mappings in a real 2-uniformly smooth and uniformly convex Banach space. We prove some strong convergence theorems under suitable conditions. The results obtained in this paper improve and extend the corresponding results announced by many others. [Copyright &y& Elsevier]

Abstract: In 2007, Huang and Zhang [L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007) 1468–1476] rediscovered normal cone metric spaces and obtained the Banach contraction principle for this setting. Later on, Rezapour and Hamlbarani [Sh. Rezapour, R. Hamlbarani, Some notes on the paper: Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 345 (2008) 719–724] showed that there are non-normal cones and that the assumption of normality is redundant. In this paper, we obtain a generalization of the Banach contraction principle to the class of convex contractions on non-normal cone metric spaces. Our result includes, as special cases, the recent results of Huang and Zhang (2007) and Rezapour and Hamlbarani (2008) . [Copyright &y& Elsevier]

Abstract: The aim of this paper is to prove common fixed point theorems for weakly compatible mappings in modified intuitionistic fuzzy metric spaces employing the common limit range property. Illustrative examples are also furnished to support our main results. Our results improve and generalize several previously known fixed point theorems of the existing literature. [Copyright &y& Elsevier]

Abstract: Common fixed point theorems for -weakly isotone increasing mappings satisfying a generalized contractive type condition under a continuous function with for each and in complete ordered partial metric spaces are proved. To illustrate our results and to distinguish them from the existing ones, we equip the paper with examples. [Copyright &y& Elsevier]

Abstract: In this paper, we study a new general iterative scheme for finding a common element of the set of solutions of finite general mixed equilibrium problems, the set of solutions of finite variational inequalities for cocoercive mappings, the set of solutions of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of fixed points of a nonexpansive semigroup in Hilbert space. Strong convergence theorems are obtained under appropriate conditions. [Copyright &y& Elsevier]

Abstract: In this paper, a class of boundary problems for second order semilinear differential inclusions is studied. By applying techniques from multivalued analysis and fixed point theorems due to Covitz–Nadler, Bohnenblust–Karlin and Schaefer, some existence results of solutions are presented for the nonlinear term which is a Lipschitz continuous, upper or lower semicontinuous multivalued map, respectively. As consequences some existence conditions of solutions are given for a class of second order semilinear differential systems. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to investigate the demiclosedness principle, the existence theorem, and convergence theorems in CAT(0) spaces for a class of mappings which is essentially wider than that of asymptotically nonexpansive mappings. Our results generalize, extend and unify the corresponding results of Dhompongsa and Panyanak [S. Dhompongsa, B. Panyanak, On -convergence theorems in CAT(0) spaces, Comput. Math. Appl., 56 (2008) 2572–2579], Osilike and Aniagbosor [M.O. Osilike, S.C. Aniagbosor, Weak and strong convergence theorems for fixed points of asymptotically nonexpansive mappings, Math. Computer Model., 32 (2000), 1181–1191], Sahu and Beg [D.R. Sahu, I. Beg, Weak and strong convergence for fixed points of nearly asymptotically non-expansive mappings, Internat. J. Modern Math., 3(2) (2008), 135–151]. [Copyright &y& Elsevier]

Abstract: Zamfirescu [T. ZamfirescuFix 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 the results of S. Banach, R. Kannan and S.K. Chatterjea. In [S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., vol. 728, 1994, pp. 183-197], the author introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we study new extensions of the Zamfirescu theorem to the context of partial metric spaces, and among other things, we give some generalized versions of the fixed point theorem of Matthews. The theory is illustrated by some examples. [Copyright &y& Elsevier]

Abstract: In this paper, the concept of set-valued contraction of Nadler type in the setting of tvs-cone spaces was introduced and a fixed point theorem in the setting of tvs-cone spaces with respect to a solid cone was proved. Obtained results extend and generalize the main results of [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific Journal of Mathematics 30 (1969) 475–488] and [D. Wardowski, On set-valued contractions of Nadler type in cone metric spaces, Applied Mathematics Letters 24 (2011) 275–278]. Two examples are given to illustrate the usability of the results. [Copyright &y& Elsevier]

Abstract: The object of this paper is to determine Hyers–Ulam–Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS. [Copyright &y& Elsevier]

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 purpose of this paper is to present some fixed point theorems for -weakly isotone increasing mappings which satisfy a generalized nonlinear contractive condition in complete ordered metric spaces. As application, we establish an existence theorem for a solution of some integral equations. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to give some new common fixed point theorems for mappings satisfying property (E.A) on cone metric spaces. And we prove the existence and uniqueness of solution for a ordinary differential equation with periodic boundary condition. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the fourth order differential equation with four-point boundary value problem is studied, where . Some sufficient conditions guaranteeing the existence of positive solution to the above four-point boundary value problem are obtained by using the Krasnosekii fixed point theorem. [Copyright &y& Elsevier]

Abstract: In this paper we consider a class of -Laplacian three-point boundary value problems on time scales. Existence criteria for at least three positive solutions are established by using a fixed point theorem for operators on a cone. An example is also presented to illustrate the applications of the obtained results. The interesting point is that the nonlinear term in the dynamic equation is associated with the first order derivative. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with a singular generalized Sturm–Liouville boundary value problem where may be singular at and/or . By applying the fixed point theorem in cones, a new and general result on the existence of positive solutions to the second order singular generalized Sturm–Liouville boundary value problem is obtained. The first order derivative is involved in the nonlinear term explicitly. [Copyright &y& Elsevier]

Abstract: In this paper, we prove the existence of mild solutions for a first order impulsive neutral evolution differential inclusion with state-dependent delay. We transform it into an integral equation and use a fixed point theorem for condensing multi-valued maps. As an application of the main theorem, we consider the case when the multi-valued nonlinearity has sub-linear growth in the state variable. [Copyright &y& Elsevier]

Abstract: In this paper, a new iterative scheme based on the extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a family of finitely nonexpansive mappings and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping is proposed. A strong convergence theorem for this iterative scheme in Hilbert spaces is established. Applications to optimization problems are given. [Copyright &y& Elsevier]

Abstract: In this paper, some iterative schemes are given to approximate a fixed point of the nonexpansive non-self-mapping and nonexpansive self-mapping. Furthermore, the strong convergence of the scheme to a fixed point is shown in a Banach space with uniformly Gâteaux differentiable norm. The theorems extend and improve some corresponding results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, Strong convergence theorems for nonexpansive nonself-mappings without boundary conditions, Nonlinear Anal. 68 (2008) 412–419], Chang et al. [S.S. Chang, H.W. Joseph Lee, C.K. Chan, On Reich’s strong convergence theorem for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 66 (2007) 2364–2374], Chidume and Chidume [C.E. Chidume, C.O. Chidume, Iterative approximation of fixed points of nonexpansive mappings, J. Math. Anal. Appl. 318 (2006) 288–295] and Suzuki [T. Suzuki, A sufficient and necessary condition for Halpern-type strong convergence to fixed point of nonexpansive mappings, Proc. Amer. Math. Society 135 (1) (2007) 99–106]. [Copyright &y& Elsevier]

Abstract: In this paper we explain the advantage of vector-valued norms and the role of matrices that are convergent to zero in the study of semilinear operator systems by means of some basic methods of nonlinear analysis: the contraction principle, Schauder’s fixed point theorem, the Leray–Schauder continuation principle and Krasnoselskii’s cone fixed point theorem. A vector version of Krasnoselskii’s theorem is also established. [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]

Abstract: The purpose of this paper is to study the strong convergence of a general iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variation inequalities for a relaxed cocoercive mapping and the set of solutions of an equilibrium problem. Our results extend recent results announced by many others. [Copyright &y& Elsevier]

Abstract: This paper aims at studying the convergence of some iteration processes for mixed variational inequalities with convex nondifferentiable functionals and -potential, -coercive, -pseudomonotone or -strongly inverse monotone operators in uniformly smooth Banach spaces. Our results generalize corresponding theorems of [I.B. Badriev, O.A. Zadvornov, A decomposition method for variational inequalities of the second kind with strongly inverse-monotone operators, Differ. Equ. 39 (7) (2003) 936–944; I.B. Badriev, O.A. Zadvornov, A.D. Lyashko, A study of variable step iterative methods for variational inequalities of the second kind, Differ. Equ. 40 (7) (2004) 971–983] and [I.B. Badriev, O.A. Zadvornov, A.M. Saddeek, On the iterative methods for solving some variational inequalities of the second kind, in: Contemporary Problems of Mathematical Modeling (Materials of the IX All-Russian School-Seminar, 8–13 September 2001, Abrau-Dyrso), Rostov University Publishers, Rostov-Un-Don, 2001, pp. 36–41]. [Copyright &y& Elsevier]

Abstract: This paper is concerned  with the existence of positive solutions to the nonhomogeneous three-point boundary value problem  of the second-order ordinary differential equation where , and are given. , and satisfying that there exists such that , and . By applying Krasnosel’skii’s fixed-point theorem in Banach spaces, some sufficient conditions guaranteeing the existence of at least one positive solution if is either superlinear or sublinear are established for the above boundary value problem. The results obtained extend and complement some known results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with pseudo-almost periodic solutions for the nonautonomous semilinear parabolic evolution equation A new existence result of mild pseudo-almost periodic solutions for the equation is obtained by using Schauder’s fixed point theorem. [Copyright &y& Elsevier]

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]

Abstract: This paper is concerned with the following discrete system,By using the theory of the fixed-point index, sufficient conditions are obtained for the existence of positive solution to the above system. [Copyright &y& Elsevier]