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Báo cáo hóa học: " Research Article Convergence Analysis for a System of Generalized Equilibrium Problems and a Countable Family of Strict Pseudocontractions"

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 Convergence Analysis for a System of Generalized Equilibrium Problems and a Countable Family of Strict Pseudocontractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 941090 20 pages doi 10.1155 2011 941090 Research Article Convergence Analysis for a System of Generalized Equilibrium Problems and a Countable Family of Strict Pseudocontractions Prasit Cholamjiak1 and Suthep Suantai1 2 1 Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand 2 Centre of Excellence in Mathematics CHE Si Ayutthaya Road Bangkok 10400 Thailand Correspondence should be addressed to Suthep Suantai scmti005@chiangmai.ac.th Received 18 October 2010 Accepted 27 December 2010 Academic Editor Jen Chih Yao Copyright 2011 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. We introduce a new iterative algorithm for a system of generalized equilibrium problems and a countable family of strict pseudocontractions in Hilbert spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common element in the solutions set of a system of generalized equilibrium problems and the common fixed points set of an infinitely countable family of strict pseudocontractions. 1. Introduction Let H be a real Hilbert space with the inner product and inducted norm II . Let C be a nonempty closed and convex subset of H. Let fk keA C X C X be a family of bifunctions and let Ak keA C H be a family of nonlinear mappings where A is an arbitrary index set. The system of generalized equilibrium problems is to find x e C such that fk x y Akx y - x 0 Vy e C k e A. 1.1 If A is a singleton then 1.1 reduces to find x e C such that f x y Ax y - x 0 Vy e C. 1.2 The solutions set of 1.2 is denoted by GEP f A . If f 0 then the solutions set of 1.2 is denoted by VI C A and if A 0 then the solutions set of 1.2 is denoted by EP f . 2 Fixed Point .