Recent Advancements in KRH-Interpolative-Type Contractions

Abstract

The focus of this paper is to conduct a comprehensive analysis of the advancements made in the understanding of Interpolative contraction, building upon the ideas initially introduced by Karapinar in 2018. In this paper, we develop the notion of Interpolative contraction mappings to the case of non-linear Kannan Interpolative, Riech Rus Ćirić interpolative and Hardy–Roger Interpolative contraction mappings based on controlled function, and prove some fixed point results in the context of controlled metric space, thereby enhancing the current understanding of this particular analysis. Furthermore, we provide a concrete example that illustrates the underlying drive for the investigations presented in this context. An application of the proposed non-linear Interpolative-contractions to the Liouville–Caputo fractional derivatives and fractional differential equations is provided in this paper.