Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 458265, 19 pages
doi:10.1155/2010/458265
Research Article

Generalized Asymptotic Pointwise Contractions and Nonexpansive Mappings Involving Orbits

Adriana Nicolae

Department of Applied Mathematics, Babeş-Bolyai University, Kogălniceanu 1, 400084 Cluj-Napoca, Romania

Received 30 September 2009; Accepted 25 November 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Adriana Nicolae. 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 give fixed point results for classes of mappings that generalize pointwise contractions, asymptotic contractions, asymptotic pointwise contractions, and nonexpansive and asymptotic nonexpansive mappings. We consider the case of metric spaces and, in particular, CAT(0) spaces. We also study the well-posedness of these fixed point problems.