Some results in cone b -metric spaces over Banach algebras

In this paper, some new fixed point results for a contractive mapping in cone b -metric spaces over Banach algebras are obtained, which extend the condition of $\rho (\alpha + \beta) \in \big[0,\displaystyle\frac{1}{s}\big)(s \ge 1)$ to ρ (α + β )∈[0,1) (ρ (x) is the spectral radius of x ). Moreover, some similar improvements in cone b-metric spaces and b-metric spaces are also obtained, which from $(\alpha + \beta) \in \big[0,\displaystyle\frac{1}{s}\big)(s \ge 1)$ to (α + β )∈[0,1). There are some examples that are given to support the results.