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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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.

Note

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1524708085

Mathematical Reviews number (MathSciNet)
MR3794319

Zentralblatt MATH identifier
06873763

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

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

Citation

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. https://projecteuclid.org/euclid.nihmj/1524708085


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References

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