Some Innovative Results for Interpolative Reich–Rus–Ćirić-Type Contractions in Rectangular m-Metric Spaces

In this paper, we study the existence of fixed points for interpolative Reich–Rus–Ćirić-type contractions in the setting of rectangular m-metric spaces. The use of the rectangular inequality, in place of the conventional triangle inequality, introduces a higher level of complexity in the computations, requiring more careful and refined analysis. We consider two distinct cases based on the sum of the interpolative exponents: one where the sum is less than 1, and another where the sum exceeds 1. The results we present generalize several existing theorems in the literature, and each is supplemented with illustrative examples to demonstrate their applicability. Moreover, we deduce corresponding results on m-metric spaces from these results, which are new themselves. They are also validated through examples.