Abstract and Applied Analysis
Volume 2010 (2010), Article ID 247402, 5 pages
doi:10.1155/2010/247402
Research Article

Remarks on Asymptotic Centers and Fixed Points

A. Kaewkhao1 and K. Sokhuma2

1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
2Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

Received 4 August 2010; Accepted 4 November 2010

Academic Editor: Mitsuharu Ôtani

Copyright © 2010 A. Kaewkhao and K. Sokhuma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a class of nonlinear continuous mappings defined on a bounded closed convex subset of a Banach space 𝑋 . We characterize the Banach spaces in which every asymptotic center of each bounded sequence in any weakly compact convex subset is compact as those spaces having the weak fixed point property for this type of mappings.