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Abstract: In this paper, we introduce viscosity approximation methods based on generalized contraction mappings for finding a set of common fixed points of a countable family of strict pseudo-contraction mappings, the common element of the set solutions of a general system of variational inequalities with Lipschitzian and relaxed cocoercive mappings and the set of solutions of a generalized mixed equilibrium problem. Furthermore, strong convergence theorems of the purposed iterative process are established in the framework of Banach spaces. The results presented in this paper improve and extend many recent important results. [Copyright &y& Elsevier]

Recently, Basha (2011) established the best proximity point theorems for proximal contractions of the first and second kinds which are extension of Banach's contraction principle in the case of non-self-mappings. The aim of this paper is to extend and generalize the notions of proximal contractions of the first and second kinds which aremore general than the notion of self-contractions, establish the existence of an optimal approximate solution theorems for these non-self-mappings, and also give examples to validate ourmain results. [ABSTRACT FROM AUTHOR]

In this paper, we prove a strong convergence theorem for finding a common solutions of a general system of variational inequalities involving two different inverse-strongly accretive operators and solutions of fixed point problems involving the nonexpansive mapping in a Banach space by using a modified viscosity extragradient method with weak contraction. Moreover, using the above results, we can apply to finding solutions of zeros of accretive operators and the class of k-strictly pseudocontractive mappings. The results presented in this paper extend and improve the corresponding results of Qin et al. [Convergence of an iterative algorithm for systems of variational inequalities and nonexpansive mappings with applications, J. Comput. Appl. Math., 233 (2009), 231-240.], Aoyama et al. [Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory and Applications, vol. 2006, Article ID 35390, 1-13.], Yao et al. [Modified extragradient methods for a system of variational inequalities in Banach spaces, Acta. Appl. Math., 110(3) (2010), 1211-1224.], Katchang et al. [A viscosity iterative scheme for inverse-strongly accretive operators in Banach spaces, Journal of Computational Analysis and Applications, 12(3) (2010), 678 686.] and many others. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly Lipschitzian continuous and asymptotically -strict pseudocontractive mapping in the intermediate sense. We prove the strong convergence theorem for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give some numerical examples for support our results. [Copyright &y& Elsevier]

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part. [ABSTRACT FROM AUTHOR]

We introduce an iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions mapping, the set of common solutions of a system of two mixed equilibrium problems and the set of common solutions of the variational inequalities with inverse strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. Finally, we apply our results for solving convex feasibility problems in Hilbert spaces. Our results improve and extend the corresponding results announced by many others recently. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we establish new coincidence and common fixed point theorems for hybrid strict contraction maps by dropping the assumption “ is -weakly commuting” for a hybrid pair of multivalued maps in Theorem 3.10 of T. Kamran (2004) . As an application, an invariant approximation result is derived. [Copyright &y& Elsevier]

We introduce a new hybrid extragradient viscosity approximation method for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for β-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality, which is the optimality condition for a minimization problem. Results obtained in this paper improve the previously known results in this area. [ABSTRACT FROM AUTHOR]

The purpose of this article is to resolve a global optimization problem for quasi-noncyclic relatively nonexpansive mappings by giving an algorithm that determines an optimal approximate solution of the following minimization problem, min x ∈ A d (x , T x) , min y ∈ B d (y , T y) and min (x , y) ∈ A × B d (x , y) ; also, we provide some illustrative examples to support our results. As an application, the existence of a solution of the analytic complex function is discussed. [ABSTRACT FROM AUTHOR]