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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 150941, 6 pages
http://dx.doi.org/10.1155/2014/150941
Research Article

Best Proximity Point for Generalized Proximal Weak Contractions in Complete Metric Space

1Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey
2Department of Mathematics, Bharathidasan University, Tiruchirappalli, Tamil Nadu 620 024, India

Received 19 September 2013; Accepted 29 October 2013; Published 16 January 2014

Academic Editor: Francis T. K. Au

Copyright © 2014 Erdal Karapınar 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 introduce a new class of nonself-mappings, generalized proximal weak contraction mappings, and prove the existence and uniqueness of best proximity point for such mappings in the context of complete metric spaces. Moreover, we state an algorithm to determine such an optimal approximate solution designed as a best proximity point. We establish also an example to illustrate our main results. Our result provides an extension of the related results in the literature.