FIXED POINT RESULTS VIA NEW GENERALIZEDRATIONAL “α∗-CONTRACTION” IN EXTENDEDb-METRIC SPACES

Abstract

In this article, we introduce the notion of α–η continuous mappings in the framework of extended b-metric spaces, which reduces to the classical b-metric space as a special case. We further propose a new class of
generalized α∗-contractions for multivalued mappings in extended b-metric spaces. Using these newly introduced concepts, we establish a fixed point theorem for multivalued generalized α∗-contractions in the setting of extended b-metric spaces. The obtained results not only extend but also unify several recent fixed point results available in the existing literature. As an application of the main theorem, we prove the existence of a solution to a Fredholm integral equation, thereby demonstrating the effectiveness of the proposed theoretical framework.