Fixed Point Theorems in Metric Spaces Induced by Coprime Relations

Abstract

In this recent study, we investigated a novel fixed point in a special metric space where the distance between two natural numbers is determined by their coprime relations. We define a metric related to the Greatest Common Divisor (GCD) and explore fixed-point results for standard coprime controlled contraction mappings and their generalizations as well as fixed point results using additional mathematical structures. With the support of artificial intelligence and we also introduced Banach, Cric, and Kannan applications with examples to illustrate this theory.