Abstract and Applied Analysis
Volume 2012 (2012), Article ID 952052, 6 pages
http://dx.doi.org/10.1155/2012/952052
Research Article

On Some Generalizations of Commuting Mappings

Mohammad Ali Alghamdi,1 Stojan Radenović,2 and Naseer Shahzad1

1Department of Mathematics, King AbdulAziz University, P.O. Box 80203, Jeddah 21859, Saudi Arabia
2Faculty of Mechanical Engineering, Kraljice Marije 16, 11 120 Beograd, Serbia

Received 16 September 2011; Revised 8 November 2011; Accepted 23 November 2011

Academic Editor: Ngai-Ching Wong

Copyright © 2012 Mohammad Ali Alghamdi 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

It is shown that occasionally 𝒥 ℋ operators as well as occasionally weakly biased mappings reduce to weakly compatible mappings in the presence of a unique point of coincidence (and a unique common fixed point) of the given maps.