Common new fixed point results on b-cone Banach spaces over Banach algebras

[EN] Recently Zhu and Zhai studied the concepts of cone b-norm and cone b-Banach space as generalizations of cone b-metric spaces and theygave a definition of φ-operator and obtained some new fixed point theorems in cone b-Banach spaces over Banach algebras by using φ-operator. In this paper we propose a notion of quasi-cone over Banach algebras, then by utilizing some new conditions and following their work with introducing two mappings T and S we improve the fixed point theorems to the commonfixed point theorems. An example is given to illustrate the usability of the obtained results.