Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2018; 33(3): 943-960

Online first article April 6, 2018      Printed July 31, 2018

https://doi.org/10.4134/CKMS.c170294

Copyright © The Korean Mathematical Society.

Some fixed-point results on parametric $N_{b}$-metric spaces

N\.{i}hal Ta\c{s}, Nihal Y\i lmaz \"{O}zg\"{u}r

Bal\i kesir University, Bal\i kesir University

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Our aim is to introduce the notion of a parametric $N_{b}$-metric and study some basic properties of parametric $N_{b}$-metric spaces. We give some fixed-point results on a complete parametric $N_{b}$-metric space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_{b}$ -metric space.

Keywords: parametric $N_{b}$-metric, \'{C}iri\'{c}'s fixed-point result, Kannan's fixed-point result, Chatterjea's fixed-point result, expansive mapping, fixed circle

MSC numbers: Primary 54H25; Secondary 47H10

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