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

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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.

Abstract

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.

참고문헌 (16)

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  11. S. Sedghi, "Common fixed point of four maps in Sb-metric spaces", J. Linear Topol. Algebra, 5(2), pp.93~104 (2016)
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  13. N. Tasand N. Y. Ozgur, "On parametric S-metric spaces and fixed-point type theorems for expansive mappings", J. Math., 2016, pp.6~ (2016)
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  16. Wolfram Research, Inc., "Mathematica, Trial Version", ~ (2017)

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