Various extensions of the Kannan fixed point theorem in C∗-algebra-valued generalized metric spaces

Abstract

This work introduce a new concept of a C^∗-algebra-valued generalized metric spaces and extend some fixed-point theorems for Kannan-type mappings in this space. The C^∗-algebra-valued generalized metric spaces recover various topological spaces, including standard generalized metric spaces and C^∗-algebra-valued metric spaces, as well as C^∗-algebra-valued b-metric spaces. Our results improve and extend a multiple recent works in the literature. We also give illustrative examples to exhibit the utility of our results. In the end, we give an application in operators equation.