Fixed point results of Hardy-Rogers and Kannan-Meir-Keeler interpolative contractions in b-metric spaces

<h2>Abstract</h2> This paper introduces innovative extensions of fixed point theory by formulating the concepts of Hardy-Rogers pairs and cyclic Kannan-Meir-Keeler type contractions in the setting of b-metric spaces through an interpolative approach. We establish new fixed point theorems that generalize and unify existing results, thereby broadening their applicability in nonlinear analysis. In particular, we prove the existence of a common fixed point for self-mappings satisfying the Hardy-Rogers pair contraction and validate our findings with illustrative examples. Additionally, we investigate cyclic mappings adhering to the Kannan-Meir-Keeler type contraction, demonstrating the existence of fixed points with further supporting examples. These findings provide novel insights into fixed point theory and expand its potential applications in mathematical analysis and related fields.