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Báo cáo hóa học: " Research Article Common Fixed Point Theorems on Weakly Contractive and Nonexpansive Mappings"

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 Common Fixed Point Theorems on Weakly Contractive and Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 469357 8 pages doi 10.1155 2008 469357 Research Article Common Fixed Point Theorems on Weakly Contractive and Nonexpansive Mappings Jian-Zhong Xiao and Xing-Hua Zhu Department of Mathematics Nanjing University of Information Science and Technology Nanjing 210044 China Correspondence should be addressed to Jian-Zhong Xiao xiaojz@nuist.edu.cn Received 8 August 2007 Accepted 26 November 2007 Recommended by Jerzy Jezierski A family of commuting nonexpansive self-mappings one of which is weakly contractive are studied. Some convergence theorems are established for the iterations of types Krasnoselski-Mann Kirk and Ishikawa to approximate a common fixed point. The error estimates of these iterations are also given. Copyright 2008 J.-Z. Xiao and X.-H. Zhu. 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 and preliminaries Let X d be a metric space and D c X. A mapping T D X is said to be nonexpansive if d Tx Ty d x y x y G D 1.1 and it is said to be weakly contractive if d Tx Ty d x y - y d x yỴ Vx y G D 1.2 where y 0 ot 0 ot is continuous and nondecreasing such that y is positive on 0 ot y 0 0 and lim t OTy f ot. It is evident that T is contractive if it is weakly contractive with y t 1 - aft where a G 0 1 and it is nonexpansive if it is weakly contractive. As an important extension of the class of contractive mappings the class of weakly contractive mappings was introduced by Alber and Guerre-Delabriere 1 . In Hilbert and Banach spaces Alber et al. 1-4 and Rhoades 5 established convergence theorems on iteration of fixed point for weakly contractive single mapping. 2 Fixed Point Theory and Applications Inspired by 2 5 6 the purpose of this paper is to study a family of commuting non-expansive mappings one of