Common Fixed Point Theorems in multiplicative $\mathfrak{m}$-metric space with Applications to the System of Multiplicative Integral Equations and Numerical Results

Abstract

This paper presents common fixed point results for a pair of self-mappings in multiplicative $\mathfrak{m}$-metric space. Also, we present the multiplicative partial metric structure as a specific case of a multiplicative m-metric space and demonstrate some common fixed point results. To support our conclusions, we present an illustrative example with discontinuous self-mappings. We also provide numerical iterations to approximate the common fixed point and graphs to visually substantiate our findings. As the consequences of our results, we demonstrate several common fixed point results in $m$-metric space and partial metric space. Our findings generalize various fixed point results from the literature. Furthermore, we employ the results to demonstrate the existence and uniqueness of solutions to a system of multiplicative Fredholm integral equations.