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 Hybrid Projection Algorithm for Finding Solutions of Mixed Equilibrium Problem and Variational Inequality Problem | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 383740 19 pages doi 2010 383740 Research Article A Hybrid Projection Algorithm for Finding Solutions of Mixed Equilibrium Problem and Variational Inequality Problem Filomena Cianciaruso 1 Giuseppe Marino 1 Luigi Muglia 1 and Yonghong Yao2 1 Dipartimento di Matematica Universita della Calabria 87036 Arcavacata di Rende CS Italy 2 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Correspondence should be addressed to Giuseppe Marino gmarino@ Received 3 June 2009 Accepted 16 September 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 Filomena Cianciaruso et al. 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 propose a modified hybrid projection algorithm to approximate a common fixed point of a fc-strict pseudocontraction and of two sequences of nonexpansive mappings. We prove a strong convergence theorem of the proposed method and we obtain as a particular case approximation of solutions of systems of two equilibrium problems. 1. Introduction In this paper we define an iterative method to approximate a common fixed point of a fc-strict pseudocontraction and of two sequences of nonexpansive mappings generated by two sequences of firmly nonexpansive mappings and two nonlinear mappings. Let us recall from 1 that the fc-strict pseudocontractions in Hilbert spaces were introduced by Browder and Petryshyn in 2 . Definition . S C C is said to be k-strict pseudocontractive if there exists fc e 0 1 such that Sx - Sy 2 x - y 2 k I - S x - I - S y 2 -XII e C. The iterative approximation problems for nonexpansive mappings asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings were studied extensively by Browder 3 Goebel and Kirk 4 Kirk 5 Liu 6 .
