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

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.