Optimal approximate solution  with best proximity point theorems via  Geraghty's cyclic contraction mapping

Chirasak Mongkolkeha; Yeol Je Cho; Poom Kumam

Chirasak Mongkolkeha
Yeol Je Cho
Poom Kumam Theoretical and Computational Science Center (TaCS) & Department of Mathematics, Faculty of Science, King Mongkut's University ofTechnology Thonburi (KMUTT). 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, THAILAND. http://orcid.org/0000-0002-5463-4581

Abstract

The main objective of this paper is to introduce the concept of a Geraghty's cyclic contraction which is a generalized cyclic contractive mapping and provide best proximity point theorems for such a mapping in complete metric space and uniformly convex Banach space. Moreover, we also give some examples to illustrate our main results.

Author Biography

Poom Kumam, Theoretical and Computational Science Center (TaCS) & Department of Mathematics, Faculty of Science, King Mongkut's University ofTechnology Thonburi (KMUTT). 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, THAILAND.

Dr. Poom Kumam received his B.S. degree in mathematics education from the Burapha University, Chonburi, Thailand, in 2000, his M.S. degree (mathematics) from the Chiang Mai University, Chiang Mai, Thailand, in 2002, under the supervision of Professor Sompong Dhompongsa, and his Ph.D. degree (mathematics) from the Naresuan University, Phitsanulok, Thailand, in 2007 .

Dr. Poom is the Associate Editor-in-Chief of the Thai Journal of Mathematics, Assistance Editors for The Journal of Nonlinear Analysis and Optimization: Theory & Applications, Editor for The Journal of Nonlinear Science and Applications (SCIE), The journal BULLETIN of the Malaysian Mathematical Sciences Society (SCIE) and The editorial board of Fixed Point Theory and Applications (July 2012-April 2015) (SCIE), Creative Mathematics and Informatics, Springerplus (SCIE) and Guest Editors of Abstract and Applied Analysis.

His research interest focuses on fixed-point theory with related with optimization problems in both pure science and applied science. Dr. Poom has over 300 scientific papers and projects either presented or published.