tailieunhanh - báo cáo hóa học:" Research Article A General Iterative Approach to Variational Inequality Problems and Optimization Problems Jong Soo Jung"

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 Approach to Variational Inequality Problems and Optimization Problems Jong Soo Jung | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 284363 20 pages doi 2011 284363 Research Article A General Iterative Approach to Variational Inequality Problems and Optimization Problems Jong Soo Jung Department of Mathematics Dong-A University Busan 604-714 Republic of Korea Correspondence should be addressed to Jong Soo Jung jungjs@ Received 4 October 2010 Accepted 14 November 2010 Academic Editor Jen Chih Yao Copyright 2011 Jong Soo Jung. 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 general iterative scheme for finding a common element of the set of solutions of variational inequality problem for an inverse-strongly monotone mapping and the set of fixed points of a nonexpansive mapping in a Hilbert space and then establish strong convergence of the sequence generated by the proposed iterative scheme to a common element of the above two sets under suitable control conditions which is a solution of a certain optimization problem. Applications of the main result are also given. 1. Introduction Let H be a real Hilbert space with inner product and induced norm II . Let C be a nonempty closed convex subset of H and S C C be self-mapping on C. We denote by F S the set of fixed points of S and by PC the metric projection of H onto C. Let A be a nonlinear mapping of C into H. The variational inequality problem is to find a u e C such that v - u Au 0 Vv e C. We denote the set of solutions of the variational inequality problem by VI C A . The variational inequality problem has been extensively studied in the literature see 1-5 and the references therein. Recently in order to study the problem coupled with the fixed point problem many authors have introduced some iterative schemes for finding a common element of the