F-cone metric spaces over Fréchet algebra

Abstract

Abstract The paper deals with the achievements of introducing the notion of F-cone metric spaces over Fréchet algebra as a generalization of F-cone metric spaces over a Banach algebra, -cone metric spaces over a Banach algebra, and -cone metric spaces over a Banach algebra. First, we study some of its topological properties. Next, we define a generalized Lipschitz for such spaces. Also, 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 work generalizes some well-known results in the literature.