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Abstract: In this paper, we study the following minimization problem where is a bounded linear operator, is some constant, is a potential function for , is the set of fixed points of nonexpansive mapping and is the solution set of an equilibrium problem. This paper introduces two new algorithms (one implicit and one explicit) that can be used to find the solution of the above minimization problem. [Copyright &y& Elsevier]

Abstract: Let be a closed convex subset of a real Hilbert space and assume that is a -strictly pseudo-contractive mapping for some such that . Consider the following iterative algorithm in given by where denotes the identity mapping on , is a mapping defined by , is the metric projection of onto , is a bounded linear strong positive operator on , is a contraction on . It is proved that the sequence generated by the above iterative algorithm converges strongly to a common fixed point of , which solves a variational inequality related to the linear operator . Our results improve and extend the results announced by [B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957–961; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486–491; A. Moudafi, Viscosity approximation methods for fixed points problems, J. Math. Anal. Appl. 241 (2000) 46–55; G. Marino, H.K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43–52] and many others. [Copyright &y& Elsevier]

Abstract: Let be a closed convex subset of a real uniformly smooth and strictly convex Banach space . Consider the following iterative algorithm given by where is a contraction on and is a mapping generated by an infinite family of nonexpansive mappings . Assume that the set of common fixed points of this infinite family of nonexpansive mappings is not empty. In this paper, we prove that the sequence generated by the above iterative algorithm converges strongly to a common fixed point of , which solves some variational inequality. Our results improve and extend the results announced by many others. [Copyright &y& Elsevier]

Fixed points of functions have applications in game theory, mathematics, physics, economics and computer science. The purpose of this article is to compute fixed points of a general quadratic polynomial in finite algebras of split quaternion and octonion over prime fields Z p . Some characterizations of fixed points in terms of the coefficients of these polynomials are also given. Particularly, cardinalities of these fixed points have been determined depending upon the characteristics of the underlying field. [ABSTRACT FROM AUTHOR]

In this paper, we introduce F-convex contraction via admissible mapping in the sense of Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 94 (2012), 6 pages] which extends convex contraction mapping of type-2 of Istrǎţescu [Some fixed point theorems for convex contraction mappings and convex non-expansive mappings (I), Libertas Mathematica, 1(1981), 151–163] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result. [ABSTRACT FROM AUTHOR]

Abstract: In this work, a projection algorithm is considered for treating strongly continuous semigroups of demicontinuous pseudocontractions. Theorems of strong convergence of fixed points are established in the framework of real Hilbert spaces. [Copyright &y& Elsevier]

Abstract: In this paper, a general system of nonlinear variational inequality problem in Banach spaces was considered, which includes some existing problems as special cases. For solving this nonlinear variational inequality problem, we construct two methods which were inspired and motivated by Korpelevich’s extragradient method. Furthermore, we prove that the suggested algorithms converge strongly to some solutions of the studied variational inequality. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an iterative method for finding a common element in the solution set of generalized equilibrium problems, in the solution set of variational inequalities and in the common fixed point set of a family of nonexpansive mappings. Strong convergence theorems are established in the framework of Hilbert spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an iterative method based on the extragradient method for finding a common element of the set of a general system of variational inequalities and the set of fixed points of a strictly pseudocontractive mapping in a real Hilbert space. Furthermore, we prove that the studied iterative method strongly converges to a common element of the set of a general system of variational inequalities and the set of fixed points of a strictly pseudocontractive mapping under some mild conditions imposed on algorithm parameters. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a general iterative scheme for finding a common element of the set of common solutions of generalized equilibrium problems, the set of common fixed points of a family of infinite non-expansive mappings. Strong convergence theorems are established in a real Hilbert space under suitable conditions. As some applications, we consider convex feasibility problems and equilibrium problems. The results presented improve and extend the corresponding results of many others. [Copyright &y& Elsevier]

In this paper, we consider the problem of convergence of an iterative algorithm for a system of generalized variational inequalities and a nonexpansive mapping. Strong convergence theorems are established in the framework of real Banach spaces. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce an explicit iterative process for a finite family of asymptotically -strict pseudo-contractions. By using the iterative process, we get a weak convergence theorem for a finite family of asymptotically -strict pseudo-contractions and then we modify these algorithms to have strong convergence in the framework of Hilbert spaces. Our results improve and extend the recent ones announced by [G.L. Acedo, H.K. Xu, Iterative methods for strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 67 (2007) 2258–2271; T.H. Kim, H.K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140–1152; C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400–2411; K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379; G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert space, J. Math. Anal. Appl. 329 (2007) 336–346; T.H. Kim, H.K. Xu, Convergence of the modified Manns iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal. (2007), doi:10.1016/j.na.2007.02.029] and many others. [Copyright &y& Elsevier]

Abstract: In this paper, we modify the normal Mann’s iterative process to have strong convergence for a -strictly pseudo-contractive non-self mapping in the framework of Hilbert spaces. Our results improve and extend the corresponding results announced by many others. [Copyright &y& Elsevier]

Abstract: In this work, an implicit iterative process is considered for asymptotically pseudocontractive nonself-mappings. Weak and strong convergence theorems for common fixed points of a family of asymptotically pseudocontractive nonself-mappings are established in the framework of Hilbert spaces. [Copyright &y& Elsevier]

Abstract: In an infinite-dimensional Hilbert space, the normal Mann’s iteration algorithm has only weak convergence, in general, even for nonexpansive mappings. In order to get a strong convergence result, we modify the normal Mann’s iterative process for an infinite family of nonexpansive mappings in the framework of Banach spaces. Our results improve and extend the recent results announced by many others. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a modified Mann iterative process for approximating a common fixed point of a finite family of strict pseudo-contractions in Hilbert spaces. We establish the strong convergence theorem of the general iteration scheme under some mild conditions. Our results extend and improve the recent ones announced by many others. [Copyright &y& Elsevier]