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Abstract and Applied Analysis
Volume 2014, Article ID 287492, 13 pages
http://dx.doi.org/10.1155/2014/287492
Research Article

Discussion on “Multidimensional Coincidence Points” via Recent Publications

1Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
3University of Jaén, Campus las Lagunillas s/n, 23071 Jaén, Spain

Received 17 March 2014; Accepted 23 March 2014; Published 8 May 2014

Academic Editor: Jen-Chih Yao

Copyright © 2014 Saleh A. Al-Mezel 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

We show that some definitions of multidimensional coincidence points are not compatible with the mixed monotone property. Thus, some theorems reported in the recent publications (Dalal et al., 2014 and Imdad et al., 2013) have gaps. We clarify these gaps and we present a new theorem to correct the mentioned results. Furthermore, we show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem.