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

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Tomar Anita; Kumar Deepak; Sharma Ritu; Joshi Meena

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Journal Paper

Paper Information

Journal: SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS (SCMA) Year:2023 | Volume:20 | Issue:4 Page(s): 205-225

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Information Journal Paper

Title

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

Author(s)

Tomar Anita | Kumar Deepak | Sharma Ritu | Joshi Meena | Issue Writer Certificate

Keywords

Fixed circle

Fixed disc

Hausdorff metric

Multi-valued mappings

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.

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