Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2004; 19(2): 321-328

Printed June 1, 2004

Copyright © The Korean Mathematical Society.

Convergence Theorems of The Iterative Sequences for Nonexpansive Mappings

Jung Im Kang, Yeol Je Cho, Haiyun Zhou

Gyeongsang National University, Gyeongsang National University, Shijiazhuang Mechanical Engineering College

Abstract

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In this paper, we will prove the following: Let $D$ be a nonempty subset of a normed linear space $X$ and $T:D\rightarrow X$ be a nonexpansive mapping. Let $\{x_n\}$ be a sequence in $D$ and $\{t_n\}$, $\{s_n\}$ be real sequences such that \roster \item"{(i)}" $0\le t_n\le t

Keywords: nonexpansive mapping, Ishikawa iterative sequence, st-rong and weak convergence theorems

MSC numbers: Primary 47H17; Secondary 47H05, 47H10

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