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Journal of Applied Mathematics
Volume 2012, Article ID 643729, 14 pages
http://dx.doi.org/10.1155/2012/643729
Research Article

Best Proximity Point Theorems for Some New Cyclic Mappings

1Department of Applied Mathematics, National Hsinchu University of Education, Taiwan
2Department of Applied Mathematics, Chung Yuan Christian University, Taiwan

Received 26 February 2012; Accepted 16 June 2012

Academic Editor: Pablo González-Vera

Copyright © 2012 Chi-Ming Chen and Chao-Hung Chen. 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

By using the stronger Meir-Keeler mapping, we introduce the concepts of the sMK-G-cyclic mappings, sMK-K-cyclic mappings, and sMK-C-cyclic mappings, and then we prove some best proximity point theorems for these various types of contractions. Our results generalize or improve many recent best proximity point theorems in the literature (e.g., Elderd and Veeramani, 2006; Sadiq Basha et al., 2011).