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Báo cáo hóa học: " Research Article Strong Convergence Theorems for an Infinite Family of Equilibrium Problems and Fixed Point Problems for an Infinite Family of Asymptotically Strict Pseudocontractions"

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 Strong Convergence Theorems for an Infinite Family of Equilibrium Problems and Fixed Point Problems for an Infinite Family of Asymptotically Strict Pseudocontractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 859032 15 pages doi 10.1155 2011 859032 Research Article Strong Convergence Theorems for an Infinite Family of Equilibrium Problems and Fixed Point Problems for an Infinite Family of Asymptotically Strict Pseudocontractions Shenghua Wang 1 Shin Min Kang 2 and Young Chel Kwun3 1 School of Applied Mathematics and Physics North China Electric Power University Baoding 071003 China 2 Department of Mathematics and RINS Gyeongsang National University Jinju 660-701 Republic of Korea 3 Department of Mathematics Dong-A University Pusan 614-714 Republic of Korea Correspondence should be addressed to Young Chel Kwun yckwun@dau.ac.kr Received 12 October 2010 Accepted 29 January 2011 Academic Editor Jong Kim Copyright 2011 Shenghua Wang 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. We prove a strong convergence theorem for an infinite family of asymptotically strict pseudocontractions and an infinite family of equilibrium problems in a Hilbert space. Our proof is simple and different from those of others and the main results extend and improve those of many others. 1. Introduction Let C be a closed convex subset of a Hilbert space H. Let S C H be a mapping and if there exists an element x e C such that x Sx then x is called a fixed point of S. The set of fixed points of S is denoted by F S . Recall that 1 S is called nonexpansive if IISx - Sy x- y x y e C 1.1 2 S is called asymptotically nonexpansive 1 if there exists a sequence kn c 1 to with kn 1 such that 2 Fixed Point Theory and Applications Snx - Sny fcn x - y x y e C n 1 1.2 3 S is called to be a K-strict pseudo-contraction 2 if there exists a constant K with 0 K 1 such that Sx - Sy 2 x - y 2 k x - y - Sx - Sy 2 x y e C 1.3 4 S is called an asymptotically K-strict .