Iterative Methods and Applications 2014

An important branch of nonlinear analysis theory, applied in the study of nonlinear phenomena, in engineering, physics, and life sciences, is related to the existence of fixed points of nonlinear mappings, to the approximation of fixed points of nonlinear operators and of zeros of nonlinear operators, and to the approximation of solutions of variational inequalities.This special issue is focused on the latest achievements on these topics and the related applications.The aim is to present newest and extended coverage of the fundamental ideas, concepts, and important results on the topics as follows: (i) new iterative schemes to approximate fixed points of nonlinear mappings, common fixed points of nonlinear mappings, or semigroups of nonlinear mappings, (ii) iterative approximations of zeros of accretive-type operators, (iii) iterative approximations of solutions of variational inequalities problems or split feasibility problems and applications, (iv) optimization problems and their algorithmic approaches, (v) methods for the global continuation of fixed point curves in engineering problems, and (vi) fixed point of nonlinear operators in cone metric spaces with applications and fixed points of nonlinear operators in ordered metric spaces with applications.We invited the authors to present their original articles that will stimulate the continuing efforts in developing new results in the previously mentioned areas.F. Zhang et al. introduce a new iterative scheme for finding a common fixed point of two countable families of multivalued quasi-nonexpansive mappings and prove a weak convergence theorem under the suitable control conditions in a uniformly convex Banach space.S. M. Kang et al. establish the strong convergence for the hybrid 𝑆-iterative scheme associated with nonexpansive and Lipschitz strongly pseudocontractive mappings in Banach spaces.R. Wangkeeree and P. Yimmuang first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem.Then they introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings.Y. Tang et al. prove strong convergence theorems for a common element of the set of fixed points of a finite family of pseudocontractive mappings and the set of solutions of a finite family of monotone mappings.The common element is the unique solution of a certain variational inequality.L.-C.Ceng et al. introduce a new relaxed viscosity approximation method with regularization and prove the strong convergence of the method to a common fixed point of finitely many nonexpansive mappings and a strict pseudocontraction that also solves a convex minimization problem and a suitable equilibrium problem.Recently, S. Takahashi and W. Takahashi proposed an iterative algorithm for finding common solutions of generalized equilibrium problems governed by inverse strongly monotone mappings and of fixed points problems for nonexpansive mappings.H. Zhang and F. Wang provide a result that

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