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Abstract and Applied Analysis
Volume 2013, Article ID 697151, 6 pages
Research Article

A Note on Various Classes of Compatible-Type Pairs of Mappings and Common Fixed Point Theorems

1Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia
2Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia
3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 , Saudi Arabia

Received 8 September 2013; Accepted 27 September 2013

Academic Editor: Wei-Shih Du

Copyright © 2013 Zoran Kadelburg 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.


Several authors have introduced various conditions which can be used in order to prove common fixed point results. However, it became clear recently that some of these conditions, though formally distinct from each other, actually coincide in the case when the given mappings have a unique point of coincidence. Hence, in fact, new common fixed point results cannot be obtained in this way. We make a review of such connections and results in this paper.