Fixed Point and Best Proximity Point Results in PIV-S-Metric Spaces

Asim, Mohammad; Imdad, Mohammad

doi:10.2478/amsil-2024-0014

Abstract

This paper presents the concept of a partial idempotent valued S-metric space, abbreviated as PIV-S-metric space, as a generalization of both the PIV-metric space and S-metric space. The study utilizes this new framework to establish a fixed point theorem and a best proximity point theorem. Additionally, the paper proves the existence and uniqueness of the best proximity point within this context. Several illustrative examples are provided to demonstrate the practical applications of the main findings.

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Fixed Point and Best Proximity Point Results in PIV-S-Metric Spaces

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