1. Multiplicative 픪-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results.
- Author
-
Yadav, Kapil and Kumar, Deepak
- Subjects
- *
INTEGRAL equations , *METRIC spaces , *CONTRACTIONS (Topology) - Abstract
The objective of this manuscript is to introduce the notion of multiplicative 픪 -metric space, inspired by the concepts of multiplicative metric space and 픪 -metric space. We propose a generalized notion of the distance function known as the multiplicative 픪 -metric. Firstly, we present the fundamental definitions for the multiplicative 픪 -metric space, then delve into the topological aspects, including the convergence of sequences and completeness. Additionally, we provide various illustrations to support our discussion. We also generalize some well-known contraction mappings and prove fixed point theorems on the complete multiplicative 픪 -metric space. To complement our findings, we have included numerical results along with graphs to provide visual support for our conclusions. Furthermore, we explore the potential of utilizing the multiplicative 픪 -metric to demonstrate the existence of the solution to a multiplicative integral equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF