|Table of Contents|

Approximating Fixed Points in Normed Linear Spaces

《南京理工大学学报》(自然科学版)[ISSN:1005-9830/CN:32-1397/N]

Issue:
2005年04期
Page:
495-497
Research Field:
Publishing date:

Info

Title:
Approximating Fixed Points in Normed Linear Spaces
Author(s):
ZHU Shun-rong
School of Sciences, NUST, Nanjing 210094,China
Keywords:
normed linear space fixed point self map closed convex subset
PACS:
O177.91
DOI:
-
Abstract:
In normed linear spaces, Ishikawa iterative sequence is used to provide three fixed point theorems. These theorems extend Pathak H K and Kang S M. s fixed point theorems. Let X be a normed linear space, E a nonempty closed, bunded convex subset of X , T : E y E , F( T) X ª . Let x 1 be any point in E , If M( x 1, An , Bn , T) converges to p , then p I F ( T) . Let X be a uniformly convex Banach space, E a closed convex subset of X and let T be self map on E . Let x 0 be any point in E , then the sequence { xn} ]n = 1 converges to p I F ( T ) ,where x n is defined, iteratively for each positive integer n by xn+ 1 = ( 1- cn) xn + cnTx n.

References:

[ 1] Ishikawa S. Fixed point by a new iteration method[ J] . Proc Amer Math Soc. , 1974, 44: 147- 150.
[ 2] Gregus D M. A fixed point theorem in Banach space[ J] . Boll Un Mat Ital, 1980, 1: 193- 198.
[ 3] Groetsch C W. A note on segmenting mann iterates [ J] . J Math Anal Appl, 1972, 40: 369- 372.

Memo

Memo:
-
Last Update: 2013-03-03