Fixed Point Theory and Applications
Volume 2006 (2006), Issue 3, Pages 35390, 13 p.
doi:10.1155/FPTA/2006/35390
Weak convergence of an iterative sequence for accretive operators in Banach spaces
Koji Aoyama1
, Hideaki Iiduka2
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
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.