Recently Zhu and Zhai studied the concepts of cone b-norm and cone b- Banach space as generalizations of cone b-metric spaces and they gave a de nition of \phi-operator and obtained some new fi xed point theorems in cone b-Banach spaces over Banach algebras by using \phi-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 fi xed point theorems to the common fi xed point theorems. An example is given to illustrate the usability of the obtained results.
