Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 815637, 25 pages
doi:10.1155/2009/815637
Research Article

Some Combined Relations between Contractive Mappings, Kannan Mappings, Reasonable Expansive Mappings, and T-Stability

M. De la Sen

Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, Campus de Leioa (Bizkaia), Apertado 644 de Bilbao, 48080 Bilbao, Spain

Received 13 May 2009; Accepted 31 August 2009

Academic Editor: Andrzej Szulkin

Copyright © 2009 M. De la Sen. 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

In recent literature concerning fixed point theory for self-mappings T:X→X in metric spaces (X,d), there are some new concepts which can be mutually related so that the inherent properties of each one might be combined for such self-mappings. Self-mappings T:X→X can be referred to, for instance, as Kannan-mappings, reasonable expansive mappings, and Picard T-stable mappings. Some relations between such concepts subject either to sufficient, necessary, or necessary and sufficient conditions are obtained so that in certain self-mappings can exhibit combined properties being inherent to each of its various characterizations.