%0 Journal Article %T A sharp generalization on cone b-metric space over Banach algebra %A Huang, Huaping %A Radenovic, Stojan %A Deng, Guantie %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 2 %@ ISSN 2008-1901 %F Huang2017 %X The aim of this paper is to generalize a famous result for Banach-type contractive mapping from \(\rho(k)\in[0,\frac{1}{s})\) to \(\rho(k)\in[0,1)\) in cone b-metric space over Banach algebra with coefficient \(s\geq 1\), where \(\rho(k)\) is the spectral radius of the generalized Lipschitz constant \(k\). Moreover, some similar generalizations for the contractive constant \(k\) from \(k\in[0,\frac{1}{s})\) to \(k \in [0, 1)\) in cone b-metric space and in b-metric space are also obtained. In addition, two examples are given to illustrate that our generalizations are in fact real generalizations. %9 journal article %R 10.22436/jnsa.010.02.09 %U http://dx.doi.org/10.22436/jnsa.010.02.09 %P 429--435