Nihonkai Mathematical Journal

Fixed point theorems for asymptotic mappings of a generalized contractive type in complete metric spaces

Masashi Toyoda and Toshikazu Watanabe

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Abstract

We consider an asymptotic version of $\alpha$-$\psi$ contractive mappings. We show the existence and uniqueness of fixed points. Caccioppoli's fixed point theorem is deduced from main results in this paper. Moreover, we discuss an asymptotic version of mappings related with $(c)$-comaprison functions.

Note

The authors would like to thank the referees for valuable suggestions and comments.

Article information

Source
Nihonkai Math. J., Volume 29, Number 1 (2018), 21-28.

Dates
Received: 22 March 2017
Revised: 11 June 2018
First available in Project Euclid: 6 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1549422081

Mathematical Reviews number (MathSciNet)
MR3908816

Zentralblatt MATH identifier
07063838

Subjects
Primary: 46A40: Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42] 47B50: Operators on spaces with an indefinite metric [See also 46C50] 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Keywords
fixed point theorem contractive mappings asymptotic contraction

Citation

Toyoda, Masashi; Watanabe, Toshikazu. Fixed point theorems for asymptotic mappings of a generalized contractive type in complete metric spaces. Nihonkai Math. J. 29 (2018), no. 1, 21--28. https://projecteuclid.org/euclid.nihmj/1549422081


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