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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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.


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

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

fixed point theorem contractive mappings asymptotic contraction


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.

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