Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 169837, 16 pages
doi:10.1155/2010/169837
Research Article

Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity

Rafa Espínola,1 Aurora Fernández-León,1 and Bożena Piątek2

1Departamento de Análisis Matemático, Universidad de Sevilla, P.O. Box 1160, 41080 Sevilla, Spain
2Institute of Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland

Received 20 April 2009; Accepted 28 May 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Rafa Espínola et al. 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 study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.