Nihonkai Mathematical Journal

Comments on some recent existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings

Tomonari Suzuki

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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.


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

Article information

Nihonkai Math. J., Volume 28, Number 2 (2017), 105-116.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20]
Secondary: 47J25: Iterative procedures [See also 65J15] 90C30: Nonlinear programming

best proximity point fixed point Kannan-type mapping Chatterjea-type mapping


Suzuki, Tomonari. Comments on some recent existence theorems of best proximity points for Kannan-type and Chatterjea-type mappings. Nihonkai Math. J. 28 (2017), no. 2, 105--116.

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