F-cone metric spaces over Banach algebra

Abstract

The paper deals with the achievement of introducing the notion of F-cone metric spaces over Banach algebra as a generalization of Np-cone metric space over Banach algebra and Nb-cone metric space over Banach algebra and studying some of its topological properties. Also, here we define generalized Lipschitz and expansive maps for such spaces. Moreover, we investigate some fixed points for mappings satisfying such conditions in the new framework. Subsequently, as an application of our results, we provide an example. Our results generalize some well-known results in the literature.