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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 130439, 5 pages
http://dx.doi.org/10.1155/2014/130439
Research Article

On Best Proximity Point Theorems without Ordering

1Department of Mathematics, Razi University, Kermanshah 67149, Iran
2Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 20 September 2013; Accepted 14 December 2013; Published 16 January 2014

Academic Editor: Calogero Vetro

Copyright © 2014 A. P. Farajzadeh 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

Recently, Basha (2013) addressed a problem that amalgamates approximation and optimization in the setting of a partially ordered set that is endowed with a metric. He assumed that if and are nonvoid subsets of a partially ordered set that is equipped with a metric and is a non-self-mapping from to , then the mapping has an optimal approximate solution, called a best proximity point of the mapping , to the operator equation , when is a continuous, proximally monotone, ordered proximal contraction. In this note, we are going to obtain his results by omitting ordering, proximal monotonicity, and ordered proximal contraction on .