Báo cáo hóa học: "Research Article A General Iterative Method for Variational Inequality Problems, Mixed Equilibrium Problems, and Fixed Point Problems of Strictly Pseudocontractive Mappings in Hilbert 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 A General Iterative Method for Variational Inequality Problems, Mixed Equilibrium Problems, and Fixed Point Problems of Strictly Pseudocontractive Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 519065 32 pages doi 2009 519065 Research Article A General Iterative Method for Variational Inequality Problems Mixed Equilibrium Problems and Fixed Point Problems of Strictly Pseudocontractive Mappings in Hilbert Spaces Rattanaporn Wangkeeree and Rabian Wangkeeree Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Rabian Wangkeeree rabianw@ Received 23 April 2009 Accepted 22 June 2009 Recommended by Anthony To Ming Lau We introduce an iterative scheme for finding a common element of the set of fixed points of a k-strictly pseudocontractive mapping the set of solutions of the variational inequality for an inverse-strongly monotone mapping and the set of solutions of the mixed equilibrium problem in a real Hilbert space. Under suitable conditions some strong convergence theorems for approximating a common element of the above three sets are obtained. As applications at the end of the paper we first apply our results to study the optimization problem and we next utilize our results to study the problem of finding a common element of the set of fixed points of two families of finitely k-strictly pseudocontractive mapping the set of solutions of the variational inequality and the set of solutions of the mixed equilibrium problem. The results presented in the paper improve some recent results of Kim and Xu 2005 Yao et al. 2008 Marino et al. 2009 Liu 2009 Plubtieng and Punpaeng 2007 and many others. Copyright 2009 R. Wangkeeree and R. Wangkeeree. 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 Throughout this paper we always assume that H is a real Hilbert space with inner product and norm II II respectively C is

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