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báo cáo hóa học:" Research Article Hybrid Proximal-Type Algorithms for Generalized Equilibrium Problems, Maximal Monotone "

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 Proximal-Type Algorithms for Generalized Equilibrium Problems, Maximal Monotone | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 973028 23 pages doi 10.1155 2011 973028 Research Article Hybrid Proximal-Type Algorithms for Generalized Equilibrium Problems Maximal Monotone Operators and Relatively Nonexpansive Mappings Lu-Chuan Zeng 1 2 Q. H. Ansari 3 and S. Al-Homidan3 1 Department of Mathematics Shanghai Normal University Shanghai 200234 China 2 Scientific Computing Key Laboratory of Shanghai Universities Shanghai 200234 China 3 Department of Mathematics and Statistics King Fahd University of Petroleum Minerals KFUPM P.O. Box 119 Dhahran 31261 Saudi Arabia Correspondence should be addressed to S. Al-Homidan homidan@kfupm.edu.sa Received 24 September 2010 Accepted 18 October 2010 Academic Editor Jen Chih Yao Copyright 2011 Lu-Chuan Zeng 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 introduce and consider new hybrid proximal-type algorithms for finding a common element of the set EP of solutions of a generalized equilibrium problem the set F S of fixed points of a relatively nonexpansive mapping S and the set T-10 of zeros of a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems for these hybrid proximal-type algorithms are established that is under appropriate conditions the sequences generated by these various algorithms converge strongly to the same point in EP n F S n T-10. These new results represent the improvement generalization and development of the previously known ones in the literature. 1. Introduction Let E be a real Banach space with the dual E and C be a nonempty closed convex subset of E. We denote by N and R the sets of positive integers and real numbers respectively. Also we denote by J the normalized duality mapping from E to