Some New Results of Interpolative Hardy–Rogers and Ćirić–Reich–Rus Type Contraction

Abstract

In this paper, we present new concepts on completeness of Hardy–Rogers type contraction mappings in metric space to prove the existence of fixed points. Furthermore, we introduce the concept of $g$ -interpolative Hardy–Rogers type contractions in $b$ -metric spaces to prove the existence of the coincidence point. Lastly, we add a third concept, interpolative weakly contractive mapping type, Ćirić–Reich–Rus, to show the existence of fixed points. These results are a generalization of previous results, which we have reinforced with examples.