Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 470141, 6 pages
doi:10.1155/2010/470141
Research Article

A Counterexample on a Theorem by Khojasteh, Goodarzi, and Razani

Ivan D. Arandelović1 and Dragoljub J. Kečkić2

1Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11000 Beograd, Serbia
2Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia

Received 27 June 2010; Revised 1 September 2010; Accepted 1 September 2010

Academic Editor: L. Górniewicz

Copyright © 2010 Ivan D. Arandelović and Dragoljub J. Kečkić. 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

In the paper by Khojasteh et al. (2010), the authors tried to generalize Branciari's theorem, introducing the new integral type contraction mappings. In this note we give a counterexample on their main statement (Theorem 2.9). Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, where the cone is taken from the infinite dimensional space.