tailieunhanh - báo cáo hóa học:" Research Article Strong Convergence for Mixed Equilibrium Problems of Infinitely Nonexpansive Mappings Jintana Joomwong"

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 for Mixed Equilibrium Problems of Infinitely Nonexpansive Mappings Jintana Joomwong | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 756492 22 pages doi 2010 756492 Research Article Strong Convergence for Mixed Equilibrium Problems of Infinitely Nonexpansive Mappings Jintana Joomwong Division of Mathematics Faculty of Science Maejo University Chiang Mai 50290 Thailand Correspondence should be addressed to Jintana Joomwong jintana@ Received 29 March 2010 Accepted 24 May 2010 Academic Editor Tomonari Suzuki Copyright 2010 Jintana Joomwong. 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 introduce a new iterative scheme for finding a common element of infinitely nonexpansive mappings the set of solutions of a mixed equilibrium problems and the set of solutions of the variational inequality for an a-inverse-strongly monotone mapping in a Hilbert Space. Then the strong converge theorem is proved under some parameter controlling conditions. The results of this paper extend and improve the results of Jing Zhao and Songnian He 2009 and many others. Using this theorem we obtain some interesting corollaries. 1. Introduction Let H be a real Hilbert space with norm II II and inner product .And let C be a nonempty closed convex subset of H. Let ỳ C R be a real-valued function and let 0 C X C R be an equilibrium bifunction that is 0 u Ù 0 for each u e C. Ceng and Yao 1 considered the following mixed equilibrium problem. Find x e C such that 0 x y ỳ y - ỳ x 0 Vy e C. The set of solutions of is denoted by MEP 0 ỳ . It is easy to see that x is the solution of problem and x e dom ỳ x e y x to . In particular if ỳ 0 the mixed equilibrium problem reduced to the equilibrium problem. Find x e C such that 0x y 0 Vy e C. 2 Fixed Point Theory and Applications The set of solutions of is denoted by EP 0 . If p 0 and G x y Ax y - x