\(\mathfrak{F}\)-Bipolar metric spaces and fixed point theorems with applications

Volume 26, Issue 2, pp 184--195 http://dx.doi.org/10.22436/jmcs.026.02.08

Publication Date: November 05, 2021 Submission Date: August 03, 2021 Revision Date: September 06, 2021 Accteptance Date: September 25, 2021

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Authors

S. Rawat - Department of Mathematics, H.N.B. Garhwal University, Uttarakhand-246174, India. R. C. Dimri - Department of Mathematics, H.N.B. Garhwal University, Uttarakhand-246174, India. A. Bartwal - Department of Mathematics, H.N.B. Garhwal University, Uttarakhand-246174, India.

Abstract

In this paper, we propose a new generalization of metric spaces by the unification of two novel notions, namely \(\mathfrak{F}\)-metric spaces and bipolar metric spaces, under the name \(\mathfrak{F}\)-bipolar metric spaces. Further, in this newly generalized notion we provide a binary topology and prove some fixed point results. As applications of our result, we prove the existence and uniqueness of solution of integral equation and the existence of a unique solution in homotopy theory. We also give some non-trivial examples to vindicate our claims. Our fixed point results extend several results in the existing literature.

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Keywords

• \(\mathfrak{F}\)-Bipolar metric spaces
• fixed point
• completeness

MSC

•  54E50
•  54A20
•  54H25

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