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: A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space | Qu and Cheng Fixed Point Theory and Applications 2011 2011 17 http content 2011 1 17 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space De-ning Qu1 2 and Cao-zong Cheng 1 Correspondence czcheng@bjut. 1College of Applied Science Beijing University of Technology Beijing 100124 PR China Full list of author information is available at the end of the article SpringerOpen0 Abstract In this paper the common solution problem P1 of generalized equilibrium problems for a system of inverse-strongly monotone mappings AfelCj and a system of bifunctions fk N i satisfying certain conditions and the common fixed-point problem P2 for a family of uniformly quasi-j-asymptotically nonexpansive and locally uniformly Lipschitz continuous or uniformly Holder continuous mappings f I are proposed. A new iterative sequence is constructed by using the generalized projection and hybrid method and a strong convergence theorem is proved on approximating a common solution of P1 and P2 in Banach space. 2000 MSC 26B25 40A05 Keywords Common solution Equilibrium problem Fixed-point problem Iterative sequence Strong convergence 1. Introduction Recently common solution problems . to find a common element of the set of solutions of equilibrium problems and or the set of fixed points of mappings and or the set of solutions of variational inequalities with their applications have been discussed. Some authors such as in references 1-7 presented various iterative schemes and showed some strong or weak convergence theorems on common solution problems in Hilbert spaces. In 2008-2009 Takahashi and Zembayashi 8 9 introduced several iterative sequences on finding a common solution of an equilibrium problem and a fixed-point problem for a relatively nonexpansive mapping and established some strong or .
