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báo cáo hóa học:" Research Article Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces"

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 Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 579725 21 pages doi 10.1155 2010 579725 Research Article Strong Convergence Theorems of Viscosity Iterative Methods for a Countable Family of Strict Pseudo-contractions in Banach Spaces Rabian Wangkeeree and Uthai Kamraksa Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Rabian Wangkeeree rabianw@nu.ac.th Received 23 June 2010 Accepted 13 August 2010 Academic Editor A. T. M. Lau Copyright 2010 R. Wangkeeree and U. Kamraksa. 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. For a countable family T 1 of strictly pseudo-contractions a strong convergence of viscosity iteration is shown in order to find a common fixed point of Fn X1 in either a p-uniformly convex Banach space which admits a weakly continuous duality mapping or a p-uniformly convex Banach space with uniformly Gateaux differentiable norm. As applications at the end of the paper we apply our results to the problem of finding a zero of accretive operators. The main result extends various results existing in the current literature. 1. Introduction Let E be a real Banach space and C a nonempty closed convex subset of E. A mapping f C C is called k-contraction if there exists a constant 0 k 1 such that f x - f y II k x - y for all x y e C. We use HC to denote the collection of all contractions on C. That is nc f f is a contraction on C . A mapping T C C is said to be A-strictly pseudo-contractive mapping see e.g. 1 if there exists a constant 0 A 1 such that IITx - TyII2 IIx - yII2 All I - T x - I - T y 2 1.1 for all x y e C. Note that the class of A-strict pseudo-contractions strictly includes the class of nonexpansive mappings which are mapping T on C such that Tx - Ty x - y for all