Abstract— In 2013, Liu and Xu introduced the concept of cone metric spaces over Banach algebras, replacing Banach spaces by Banach algebras. They proved some fixed point theorems in these spaces. Xu and Radenovic gave another proof for the results of Liu and Xu where the cone didn’t have the normality. In this paper we prove a new fixed point theorem for quasi - contractive mappings in cone metric space over Banach algebras. As an application of the main result, we give an example. Also the map in this example satisfies the conditions of our theorem but not the conditions of theorems of Liu and Xu and Xu amd Radenovic and it has a fixed point.

Index Terms—Banach algebra, cone metric space, fixed point, quasi – contractive mapping.

The authors are with University of Tirana, Faculty of Natural Science, Department of Mathematics, Tirana, Albania (email: erjola.liftaj@fshn.edu.al).

Cite: Eriola Sila, Elida Hoxha, Silvana Liftaj, "A Fixed Point Theorem for Quasi – Contractive Mappings on Cone Metric Space with Banach Algebras without Assumption of Normality," International Journal of Applied Physics and Mathematics vol. 9, no. 3, pp. 127-134, 2019.