Abstract and Applied Analysis
Volume 2012 (2012), Article ID 896912, 19 pages
http://dx.doi.org/10.1155/2012/896912
Research Article

Generalized Proximal -Contraction Mappings and Best Proximity Points

Winate Sanhan,1,2 Chirasak Mongkolkeha,1,3 and Poom Kumam3

1Department of Mathematics, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, King Mongkut's, University of Technology Thonburi (KMUTT), Bangmod, Thrungkru, Bangkok 10140, Thailand

Received 19 July 2012; Accepted 24 September 2012

Academic Editor: Haiyun Zhou

Copyright © 2012 Winate Sanhan 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 generalized the notion of proximal contractions of the first and the second kinds and established the best proximity point theorems for these classes. Our results improve and extend recent result of Sadiq Basha (2011) and some authors.