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Báo cáo hóa học: " Research Article New Iterative Scheme for Finite Families of Equilibrium, Variational Inequality, and Fixed Point Problems in Banach Spaces"

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 New Iterative Scheme for Finite Families of Equilibrium, Variational Inequality, and Fixed Point Problems in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 372975 18 pages doi 10.1155 2011 372975 Research Article New Iterative Scheme for Finite Families of Equilibrium Variational Inequality and Fixed Point Problems in Banach Spaces Shenghua Wang1 2 and Caili Zhou3 1 School of Applied Mathematics and Physics North China Electric Power University Baoding 071003 China 2 Department of Mathematics Gyeongsang National University Jinju 660-714 Republic of Korea 3 College of Mathematics and Computer Hebei University Baoding 071002 China Correspondence should be addressed to Shenghua Wang sheng-huawang@hotmail.com Received 6 December 2010 Accepted 30 January 2011 Academic Editor S. Al-Homidan Copyright 2011 S. Wang and C. Zhou. 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 introduced a new iterative scheme for finding a common element in the set of common fixed points of a finite family of quasi-ỷ-nonexpansive mappings the set of common solutions of a finite family of equilibrium problems and the set of common solutions of a finite family of variational inequality problems in Banach spaces. The proof method for the main result is simplified under some new assumptions on the bifunctions. 1. Introduction Throughout this paper let R denote the set of all real numbers. Let E be a smooth Banach space and E the dual space of E. The function ộ E X E R is defined by ệ x y x 2 - y Jx y 2 Nx y e E L1 where J is the normalized dual mapping from E to E defined by J x Ịx e E x x x 2 x 2 Vx e E. 1.2 2 Fixed Point Theory and Applications Let C be a nonempty closed and convex subset of E. The generalized projection n E C is a mapping that assigns to an arbitrary point x e E the minimum point of the function ộ x y that is nCx x where x is the solution to the minimization problem x x inf ộ z