tailieunhanh - Báo cáo hóa học: " Research Article A New Hybrid Algorithm for Variational Inclusions, Generalized Equilibrium Problems, and a Finite Family of Quasi-Nonexpansive Mappings"

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 A New Hybrid Algorithm for Variational Inclusions, Generalized Equilibrium Problems, and a Finite Family of Quasi-Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 350979 20 pages doi 2009 350979 Research Article A New Hybrid Algorithm for Variational Inclusions Generalized Equilibrium Problems and a Finite Family of Quasi-Nonexpansive Mappings Prasit Cholamjiak and Suthep Suantai Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand Correspondence should be addressed to Suthep Suantai scmti005@ Received 12 June 2009 Accepted 28 September 2009 Recommended by Naseer Shahzad We proposed in this paper a new iterative scheme for finding common elements of the set of fixed points of a finite family of quasi-nonexpansive mappings the set of solutions of variational inclusion and the set of solutions of generalized equilibrium problems. Some strong convergence results were derived by using the concept of W-mappings for a finite family of quasi-nonexpansive mappings. Strong convergence results are derived under suitable conditions in Hilbert spaces. Copyright 2009 P. Cholamjiak and S. Suantai. 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 H be a real Hilbert space with inner product and inducted norm II II and let C be a nonempty closed and convex subset of H. Then a mapping T C C is said to be 1 nonexpansive if Tx - Ty x - yU for all x y e C 2 quasi-nonexpansive if Tx - p x - pl I for all x e C and p e F T 3 L-Lipschitzian if there exists a constant L 0 such that Tx - Ty L x - y for all x y e C. We denoted by F T the set of fixed points of T. In 1953 Mann 1 introduced the following iterative procedure to approximate a fixed point of a nonexpansive mapping T in a Hilbert space H xn 1 anxn 1 - ữn Txn Nn e N where the initial point x0 is taken in C arbitrarily and an is a sequence in 0 1 . 2 Fixed .