Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 169837, 16 pages
doi:10.1155/2010/169837
Fixed points of single- and set-valued mappings in uniformly convex metric spaces with no metric convexity
Rafa Espínola
, Aurora Fernández-León2
and Bożena Pi\c{a}tek3
2Departamento de Análisis Matemático, Universidad de Sevilla, P.O. Box 1160, 41080 Sevilla, Spain
3Institute of Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
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.