Translator Disclaimer
2012 Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
P. Pasom, B. Panyanak
J. Appl. Math. 2012(SI03): 1-17 (2012). DOI: 10.1155/2012/327434

Abstract

Let C be a nonempty bounded closed convex subset of a complete CAT(0) space X . We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence { x k } k = 1 defined by x k + 1 = ( 1 - t m k ) x k t m k T m n k y ( m - 1 ) k ,  y ( m - 1 ) k = ( 1 - t ( m - 1 ) k ) x k t ( m - 1 ) k T m - 1 n k y ( m - 2 ) k , y ( m - 2 ) k = ( 1 - t ( m - 2 ) k ) x k t ( m - 2 ) k T m - 2 n k y ( m - 3 ) k , , y 2 k = ( 1 - t 2 k ) x k t 2 k T 2 n k y 1 k , y 1 k = ( 1 - t 1 k ) x k t 1 k T 1 n k y 0 k , y 0 k = x k , k N , converges to a common fixed point of T 1 , T 2 , , T m where they are asymptotic pointwise nonexpansive mappings on C , { t i k } k = 1 are sequences in [ 0,1 ] for all i = 1,2 , , m, and { n k } is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.

Citation

Download Citation

P. Pasom. B. Panyanak. "Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces." J. Appl. Math. 2012 (SI03) 1 - 17, 2012. https://doi.org/10.1155/2012/327434

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1295.47060
MathSciNet: MR2880853
Digital Object Identifier: 10.1155/2012/327434

Rights: Copyright © 2012 Hindawi

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.2012 • No. SI03 • 2012
Back to Top