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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 Hybrid Projection Algorithms for Generalized Equilibrium Problems and Strictly | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 312602 18 pages doi 10.1155 2010 312602 Research Article Hybrid Projection Algorithms for Generalized Equilibrium Problems and Strictly Pseudocontractive Mappings Jong Kyu Kim 1 Sun Young Cho 2 and Xiaolong Qin3 1 Department of Mathematics Education Kyungnam University Masan 631-701 Republic of Korea 2 Department of Mathematics Gyeongsang National University Chinju 660-701 Republic of Korea 3 Department of Mathematics Hangzhou Normal University Hangzhou 310036 China Correspondence should be addressed to Jong Kyu Kim jongkyuk@kyungnam.ac.kr Received 12 October 2009 Accepted 19 July 2010 Academic Editor Andras Ronto Copyright 2010 Jong Kyu Kim 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. The purpose of this paper is to consider the problem of finding a common element in the solution set of equilibrium problems and in the fixed point set of a strictly pseudocontractive mapping. Strong convergence of the purposed hybrid projection algorithm is obtained in Hilbert spaces. 1. Introduction and Preliminaries Let H be a real Hilbert space with inner product and norm II II. Let C be a nonempty closed convex subset of H and S C C a nonlinear mapping. In this paper we use F S to denote the fixed point set of S. Recall that the mapping S is said to be nonexpansive if Sx- Sy x- y x y e C. 1.1 S is said to be k-strictly pseudocontractive if there exists a constant k e 0 1 such that Sx - Sy 2 x - y 2 k x - Sx - y - Sy 2 x y e C. 1.2 S is said to be pseudocontractive if Sx - Sy 2 x - y 2 x - Sx - y - Sy 2 Nx y e C. 1.3 2 Journal of Inequalities and Applications The class of strictly pseudocontractive mappings was introduced by Browder and Petryshyn 1 in 1967. It is easy to see that the class of strictly .
