doi: 10.17706/ijapm.2019.9.3.127-134
A Fixed Point Theorem for Quasi – Contractive Mappings on Cone Metric Space with Banach Algebras without Assumption of Normality
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Silvana Liftaj
- University of Tirana, Faculty of Natural Science, Department of Mathematics, Tirana, Albania
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.
Keywords
- Banach algebra
- cone metric space
- fixed point
- quasi – contractive mapping
How to Cite
Eriola Sila, Elida Hoxha, and 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. https://doi.org/ 10.17706/ijapm.2019.9.3.127-134
Copyright & License
Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).