New fixed point theorems in cone metric spaces over Banach algebras

In the present paper the concept of α-admissible mapping for the vector version is introduced and several fixed point theorems are obtained for contractive mappings with α-admissible mappings in cone metric spaces over Banach algebras without assumption of normality of cones. There are significant improvements over other results in the literature. Further, an example is given to illustrate the main assertions.