Results via Partial-$b$ Metric and Solution of a Pair of Elliptic Boundary Value Problem

Tomar, Anita; Kumar, Deepak; Sharma, Ritu; Joshi, Meena

doi:10.22130/scma.2023.563638.1187

Document Type : Research Paper

Authors

¹ Department of Mathematics, Pt. L. M. S. Campus, Sridev Suman Uttarakhand University, Rishikesh-249201, Uttarakhand, India.

² Department of Mathematics, Lovely Professional University, Phagwara, Punjab-144411, India.

³ G.I.C. Gheradhar (Dogi) Tehri Garhwal (Uttrakhand), India.

⁴ Department of Mathematics, S. S. J. Campus, Soban Singh Jeena University Almora-263601, Uttarakhand, India.

https://doi.org/10.22130/scma.2023.563638.1187

Abstract

We give a method to establish a fixed point via partial $b$-metric for multivalued mappings. Since the geometry of multivalued fixed points perform a significant role in numerous real-world problems and is fascinating and innovative, we introduce the notions of fixed circle and fixed disc to frame hypotheses to establish fixed circle/ disc theorems in a space that permits non-zero self-distance with a coefficient more significant than one. Stimulated by the reality that the fixed point theorem is the frequently used technique for solving boundary value problems, we solve a pair of elliptic boundary value problems. Our developments cannot be concluded from the current outcomes in related metric spaces. Examples are worked out to substantiate the validity of the hypothesis of our results.

Keywords

20.1001.1.23225807.2023.20.4.13.1

Main Subjects

Fixed Point Theory

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Sahand Communications in Mathematical Analysis

Results via Partial-$b$ Metric and Solution of a Pair of Elliptic Boundary Value Problem

References

References

Volume 20, Issue 4
September 2023
Pages 205-225

Results via Partial-$b$ Metric and Solution of a Pair of Elliptic Boundary Value Problem

References

References

Volume 20, Issue 4September 2023Pages 205-225

Volume 20, Issue 4
September 2023
Pages 205-225