Best Proximity Point Theorems on b − Multiplicative Metric Spaces

Abstract

Objectives: To introduce b - multiplicative metric spaces and cyclic multiplicative rational contractions within the framework of best proximity point theorems. Methods: We define b - multiplicative metric spaces and prove best proximity point theorems for multiplicative proximal contractions, including the first and second kind, cyclic multiplicative rational contraction which extend banach's contraction principle to non-self mappings. Findings: In b - multiplicative metric spaces, the research proved the existence and uniqueness of the best proximity points for multiplicative proximal contractions of the first and second kind. We have also introduced cyclic multiplicative rational contractions. Novelty: The novelty of this work lies in introducing b-multiplicative metric spaces in the study of best proximity points and cyclic multiplicative rational contractions, thereby broadening the scope of proximity point theorems.