TAILIEUCHUNG - Báo cáo hóa học: " Research Article The Shrinking Projection Method for Common Solutions of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Strictly Pseudocontractive 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 The Shrinking Projection Method for Common Solutions of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Strictly Pseudocontractive Mappings | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011 Article ID 840319 25 pages doi 2011 840319 Research Article The Shrinking Projection Method for Common Solutions of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Strictly Pseudocontractive Mappings Thanyarat Jitpeera and Poom Kumam Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi KMUTT Bangmod Bangkok 10140 Thailand Correspondence should be addressed to Poom Kumam Received 21 September 2010 Revised 14 December 2010 Accepted 20 January 2011 Academic Editor Jewgeni Dshalalow Copyright 2011 T. Jitpeera and P. Kumam. 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 the shrinking hybrid projection method for finding a common element of the set of fixed points of strictly pseudocontractive mappings the set of common solutions of the variational inequalities with inverse-strongly monotone mappings and the set of common solutions of generalized mixed equilibrium problems in Hilbert spaces. Furthermore we prove strong convergence theorems for a new shrinking hybrid projection method under some mild conditions. Finally we apply our results to Convex Feasibility Problems CFP . The results obtained in this paper improve and extend the corresponding results announced by Kim et al. 2010 and the previously known results. 1. Introduction Let H be a real Hilbert space with inner product and norm II II and let E be a nonempty closed convex subset of H. Let T E E be a mapping. In the sequel we will use F T to denote the set of fixed points of T that is F T x e E Tx x . We denote weak convergence and strong convergence by notations and respectively. Let S E E be a mapping. Then S is called 1 nonexpansive if Sx - Sy x - y x y e E 2 .

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