Fixed Point Results Using a Three-Point Analogue of Contraction in Multiplicative $\mathfrak{m}$-Metric Spaces: Applications and Numerical Results

Multiplicative calculus emerged as an efficient alternate to the traditional calculus and provided a novel insights to the generalized metric structures. In accordance with this, we present a novel approach for fixed point results within the framework of multiplicative $\mathfrak{m}$-metric spaces, characterized by a three-point analogue of contraction mappings. The condition of continuity of these mappings is not essential in this structure, as it is in the usual metric space. %Although these mappings may not be continuous in this structure, they still possess fixed points (that is not the case in the usual metric). We extend our findings to check the existence of common fixed points for a triplet of self-mappings. To support our results, we provide illustrative examples. Our results generalize several fixed point theorems in the existing literature. Additionally, we explore the application of these findings to ascertain the existence of solutions for a multiplicative initial value problem. We additionally provide numerical iterations to estimate the common fixed point, accompanied by the graphs that visually substantiate our results.