Best proximity point theorems for generalized \(\alpha\)-proximal contractions in Banach spaces

Volume 10, Issue 9, pp 4789--4798 http://dx.doi.org/10.22436/jnsa.010.09.21

Publication Date: September 15, 2017 Submission Date: June 14, 2016

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Authors

Somayya Komal - Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. Poom Kumam - Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. - KMUTT-Fixed Point Theory and ApplicationsResearch Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan. Phatiphat Thounthong - Renewable Energy Research Centre, King Mongkut’s University of Technology North Bangkok (KMUTNB), , Wongsawang, Bangsue, Bangkok 10800, Thailand. - Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkuts University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand. Kanokwan Sitthithakerngkiet - Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok (KMUTNB), 1518 Pracharat 1 Rd., Wongsawang, Bangsue, Bangkok 10800, Thailand.

Abstract

In this paper, we obtain the best proximity point theorem for \(\alpha\)-proximal contraction of the first and second kinds in Banach spaces by using fixed point theorems. Also, we mention an example for justification of our results.

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Keywords

• Best proximity point
• generalized \(\alpha\)-proximal contraction of the first and second kinds
• approximatively compactness.

MSC

•  47H10
•  54H25

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