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 An Iterative Algorithm Combining Viscosity Method with Parallel Method for a Generalized Equilibrium Problem and Strict Pseudocontractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 794178 21 pages doi 2009 794178 Research Article An Iterative Algorithm Combining Viscosity Method with Parallel Method for a Generalized Equilibrium Problem and Strict Pseudocontractions Jian-Wen Peng 1 Yeong-Cheng Liou 2 and Jen-Chih Yao3 1 College of Mathematics and Computer Science Chongqing Normal University Chongqing 400047 China 2 Department of Information Management Cheng Shiu University Kaohsiung Taiwan 833 Taiwan 3 Department of Applied Mathematics National Sun Yat-sen University Kaohsiung Taiwan 804 Taiwan Correspondence should be addressed to Yeong-Cheng Liou simplex_liou@ Received 5 August 2008 Accepted 4 January 2009 Recommended by Hichem Ben-El-Mechaiekh We introduce a new approximation scheme combining the viscosity method with parallel method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a family of finitely strict pseudocontractions. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result we also get some new and interesting results. The results in this paper extend and improve some well-known results in the literature. Copyright 2009 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 Let H be a real Hilbert space with inner product and induced norm II II and let C be a nonempty-closed convex subset of H. Let p H R u X be a function and let F be a bifunction from C X C to R such that C n dom p 0 where R is the set of real numbers and dom p x e H y x X . Flores-Bazan 1 introduced the following generalized equilibrium problem Find x e C such that F x ỳ y y y x Ny 6 C. The set of solutions of is .
