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 Iterative Algorithms for Finding Common Solutions to Variational Inclusion Equilibrium and Fixed Point Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 915629 17 pages doi 2011 915629 Research Article Iterative Algorithms for Finding Common Solutions to Variational Inclusion Equilibrium and Fixed Point Problems J. F. Tan and S. S. Chang Department of Mathematics Yibin University Yibin Sichuan 644007 China Correspondence should be addressed to S. S. Chang changss@ Received 30 October 2010 Accepted 9 November 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 J. F. Tan and S. S. Chang. 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. The main purpose of this paper is to introduce an explicit iterative algorithm to study the existence problem and the approximation problem of solution to the quadratic minimization problem. Under suitable conditions some strong convergence theorems for a family of nonexpansive mappings are proved. The results presented in the paper improve and extend the corresponding results announced by some authors. 1. Introduction Throughout this paper we assume that H is a real Hilbert space with inner product and norm II II C is a nonempty closed convex subset of H and F T x e H Tx x is the set of fixed points of mapping T. A mapping S C C is called nonexpansive if Sx - Sy x - y Yx y e C. Let A H H be a single-valued nonlenear mapping and M H 2h be a multivalued mapping. The so-called quasivariational inclusion problem see 1-3 is to find u e H such that e e A u M u . The set of solutions to quasivariational inclusion problem is denoted by VI H A M . 2 Fixed Point Theory and Applications Special Cases I If M dộ H 2H where ộ H R J i is a proper convex lower semi-continuous function and dộ is the subdifferential of ộ then the quasivariational inclusion problem is equivalent to finding u e H such that A u y - u ộ y -
