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Báo cáo hóa học: "Research Article Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2008 Article ID 720371 15 pages doi 10.1155 2008 720371 Research Article Common Solutions of an Iterative Scheme for Variational Inclusions Equilibrium Problems and Fixed Point Problems Jian-Wen Peng 1 Yan Wang 1 David S. Shyu 2 and Jen-Chih Yao3 1 College of Mathematics and Computer Science Chongqing Normal University Chongqing 400047 China 2 Department of Finance National Sun Yat-Sen University Kaohsiung 80424 Taiwan 3 Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung 80424 Taiwan Correspondence should be addressed to David S. Shyu dshyu@cm.nsysu.edu.tw Received 24 October 2008 Accepted 6 December 2008 Recommended by Ram U. Verma We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. The results in this paper unify extend and improve some well-known results in the literature. Copyright 2008 Jian-Wen Peng et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Throughout this paper we always assume that H is a real Hilbert space with norm and inner product denoted by - and respectively. 2H denotes the family of all the nonempty subsets of H. Let A H H be a single-valued nonlinear mapping and M H 2H be a setvalued mapping. We consider the following variational inclusion which is to find a point u e H such that e e A u M u 1.1 where e is the zero vector in H. The set of solutions of problem 1.1 is denoted by I A M