Convergence analysis of fixed point iterations in multiplicative metric spaces: A comprehensive study of mapping properties

Abstract

This paper presents a comprehensive investigation of fixed point theorems in multiplicative metric spaces with various types of contractive mappings. We establish convergence criteria for iterative sequences and prove the existence and uniqueness of fixed points under different contraction conditions. The study introduces novel results for multiplicative metric spaces and extends classical fixed point theorems to this non-Newtonian calculus framework. We examine contractive mappings, expansive mappings, and hybrid mappings, providing detailed convergence analysis with rate estimates. Applications to nonlinear integral equations and differential equations in multiplicative calculus are demonstrated. Our findings contribute to the theoretical foundation of fixed point theory in multiplicative metric spaces and offer practical tools for solving equations in exponential frameworks.