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 Viscosity Approximation to Common Fixed Points of Families of Nonexpansive Mappings with Weakly Contractive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 476913 8 pages doi 2010 476913 Research Article Viscosity Approximation to Common Fixed Points of Families of Nonexpansive Mappings with Weakly Contractive Mappings A. Razani1 2 and S. Homaeipour1 1 Department of Mathematics Faculty of Science Imam Khomeini International University . Box 34149-16818 Qazvin Iran 2 School of Mathematics Institute for Research in Fundamental Sciences . Box 19395-5746 Tehran Iran Correspondence should be addressed to S. Homaeipour s_homaeipour@ Received 5 June 2010 Accepted 26 July 2010 Academic Editor Brailey Sims Copyright 2010 A. Razani and S. Homaeipour. 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. Let X be a reflexive Banach space which has a weakly sequentially continuous duality mapping. In this paper we consider the following viscosity approximation sequence xn Xnf fxn 1-Xn Tnxn where xn e 0 1 Tn is a uniformly asymptotically regular sequence and f is a weakly contractive mapping. Strong convergence of the sequence xn is proved. 1. Introduction Let C be a nonempty closed convex subset of a Banach space X. Recall that a self-mapping T C C is nonexpansive if T x - T y II Hx - y x y e C. Alber and Guerre-Delabriere 1 defined the weakly contractive maps in Hilbert spaces and Rhoades 2 showed that the result of 1 is also valid in the complete metric spaces as follows. Definition . Let fX d be a complete metric space. A mapping T X X is called weakly contractive if d Tx Ty d x y - y d x y fi 2 Fixed Point Theory and Applications where x y e X and y 0 to 0 to is a continuous and nondecreasing function such that y f 0 if and only if t 0 and limtTO ịi f to. Theorem . Let T X X be a weakly contractive mapping where X d is a complete metric space .
