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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 235731, 8 pages
http://dx.doi.org/10.1155/2014/235731
Research Article

An Illusion: “A Suzuki Type Coupled Fixed Point Theorem”

1Nonlinear Analysis and Applied Mathematics Research Group (NAAM), King Abdulaziz University, Jeddah, Saudi Arabia
2Department of Mathematics, Atilim University, İncek 06836, Ankara, Turkey
3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
4University of Jaén, Campus las Lagunillas s/n, 23071 Jaén, Spain

Received 31 May 2014; Accepted 26 June 2014; Published 27 August 2014

Academic Editor: Wei-Shih Du

Copyright © 2014 Hamed H. Alsulami 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 admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014)] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Ðoric and Lazović (2011)] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (, r)-admissible contractions.