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International Journal of Mathematics and Mathematical Sciences
Volume 2007, Article ID 39281, 6 pages
http://dx.doi.org/10.1155/2007/39281
Research Article

Meir-Keeler Contractions of Integral Type Are Still Meir-Keeler Contractions

Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Tobata, Kitakyushu 804-8550, Japan

Received 20 August 2006; Revised 27 October 2006; Accepted 5 December 2006

Academic Editor: Sehie Park

Copyright © 2007 Hindawi Publishing Corporation. 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 prove that the recent fixed point theorem for contractions of integral type due to Branciari is a corollary of the famous Meir-Keeler fixed point theorem. We also prove that Meir-Keeler contractions of integral type are still Meir-Keeler contractions.