Open Access
2017 Comments on some recent existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings
Tomonari Suzuki
Nihonkai Math. J. 28(2): 105-116 (2017).

Abstract

In 2013, Basha, Shahzad and Jeyaraj proved two existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings. In this paper, in order to clarify the mathematical structure of these theorems, we improve these theorems in the aspects of both statements and proofs. Indeed, we give very simple proofs of these theorems. We also discuss the best possibility on the numbers that appear in these theorems.

Funding Statement

The author is supported in part by JSPS KAKENHI Grant Number 16K05207 from Japan Society for the Promotion of Science.

Citation

Download Citation

Tomonari Suzuki. "Comments on some recent existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings." Nihonkai Math. J. 28 (2) 105 - 116, 2017.

Information

Received: 31 January 2017; Published: 2017
First available in Project Euclid: 26 April 2018

zbMATH: 06873763
MathSciNet: MR3794319

Subjects:
Primary: 54H25
Secondary: 47J25 , 90C30

Keywords: Best proximity point , Chatterjea-type mapping , fixed point , Kannan-type mapping

Rights: Copyright © 2017 Niigata University, Department of Mathematics

Vol.28 • No. 2 • 2017
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