Journal of Applied Mathematics
Volume 2013 (2013), Article ID 101439, 6 pages
Research Article

Existence and Convergence Theorems of Best Proximity Points

1Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 22 February 2013; Accepted 16 April 2013

Academic Editor: Gue Myung Lee

Copyright © 2013 Moosa Gabeleh and Naseer Shahzad. 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.


The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.