# A sharp generalization on cone b-metric space over Banach algebra

Volume 10, Issue 2, pp 429--435
Publication Date: February 20, 2017 Submission Date: October 29, 2016
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### Authors

Huaping Huang - School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China. Stojan Radenovic - Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia. Guantie Deng - School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China.

### Abstract

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.

### Keywords

• Cone b-metric space over Banach algebra
• fixed point
• c-sequence
• iterative sequence.

•  47H10
•  54H25

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