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 Theorem by Monotone Hybrid Algorithm for Equilibrium Problems, Hemirelatively Nonexpansive Mappings, and Maximal Monotone Operators | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 617248 12 pages doi 2008 617248 Research Article Strong Convergence Theorem by Monotone Hybrid Algorithm for Equilibrium Problems Hemirelatively Nonexpansive Mappings and Maximal Monotone Operators Yun Cheng and Ming Tian College of Science Civil Aviation University of China Tianjin 300300 China Correspondence should be addressed to Yun Cheng mathscy@ Received 17 June 2008 Accepted 11 November 2008 Recommended by Wataru Takahashi We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of hemirelatively nonexpansive mappings and the set of solutions of an equilibrium problem and for finding a common element of the set of zero points of maximal monotone operators and the set of solutions of an equilibrium problem in a Banach space. Using this theorem we obtain three new results for finding a solution of an equilibrium problem a fixed point of a hemirelatively nonexpnasive mapping and a zero point of maximal monotone operators in a Banach space. Copyright 2008 Y. Cheng and M. Tian. 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 E be a Banach space let C be a closed convex subset of E and let f be a bifunction from C X C to R where R is the set of real numbers. The equilibrium problem is to find x e C such that f x ý 0 Vy e C. The set of such solutions x is denoted by EP f . In 2006 Martinez-Yanes and Xu 1 obtained strong convergence theorems for finding a fixed point of a nonexpansive mapping by a new hybrid method in a Hilbert space. In particular Takahashi and Zembayashi 2 established a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a .
