tailieunhanh - Báo cáo hóa học: " Research Article Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive"

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 Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractiveb | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 672301 13 pages doi 2008 672301 Research Article Weak Convergence Theorems of Three Iterative Methods for Strictly Pseudocontractive Mappings of Browder-Petryshyn Type Ying Zhang and Yan Guo School of Mathematics and Physics North China Electric Power University Baoding Hebei 071003 China Correspondence should be addressed to Ying Zhang spzhangying@ Received 25 September 2007 Revised 29 January 2008 Accepted 28 February 2008 Recommended by Huang Nan-Jing Let E be a real q-uniformly smooth Banach space which is also uniformly convex . Lp or lp spaces 1 p to and K a nonempty closed convex subset of E. By constructing nonexpansive mappings we elicit the weak convergence of Mann s algorithm for a K-strictly pseudocontractive mapping of Browder-Petryshyn type on K in condition thet the control sequence an is chosen so that i p an 1 n 0 ii y 0 1 - an qK - Cq 1 -an q-1 TO where p e max 0 1 - qK Cq 1 q-1 1 . Moreover we consider to find a common fixed point of a finite family of strictly pseudocontractive mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms. Copyright 2008 Y. Zhang and Y. Guo. 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 Let E be a real Banach space and let Jq q 1 denote the generalized duality mapping from E into 2E given by Jq x f e E x f x q and f II x q-1 where E denotes the dual space of E and denotes the generalized duality pairing. In particular J2 is called the normalized duality mapping and it is usually denoted by J. If E is strictly convex then Jq is single-valued. In the sequel we will denote the single-valued generalized duality mapping by jq and F T x e E Tx x . Definition .