Analytic and Statistical Convergence Properties in Multiplicative Metric Spaces: A Logarithmic Perspective

Abstract

In this paper, we revisit the structure of multiplicative metric spaces and investigate analytic notions such as convergence, Cauchy sequences, boundedness, and density within this framework. We extend these concepts to their statistical counterparts, including statistical convergence, statistical Cauchy sequences, statistical boundedness, and statistical density. Utilizing the logarithmic isomorphism between multiplicative and classical metrics, we introduce a new definition of statistical convergence in the multiplicative setting that is equivalent to the classical one. Several theorems are established and supported by examples, demonstrating that when the generator of the multiplicative metric is the identity function, the results reduce to those in standard metric spaces. Our findings reveal a deep connection between multiplicative calculus and classical analysis, with implications for summability theory and iterative methods.