Fixed Point Theory and Applications
Volume 2006 (2006), Article ID 35390, 13 pages
doi:10.1155/FPTA/2006/35390

Weak convergence of an iterative sequence for accretive operators in Banach spaces

Koji Aoyama,1 Hideaki Iiduka,2 and Wataru Takahashi2

1Department of Economics, Chiba University, Yayoi-Cho, Inage-Ku,Chiba-Shi, Chiba 263-8522, Japan
2Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-Ku, Tokyo 152-8522, Japan

Received 21 November 2005; Accepted 6 December 2005

Copyright © 2006 Koji Aoyama 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.

Abstract

Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u∈C such that 〈Au,J(v−u)〉≥0 for all v∈C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.