Geodesic
A sharp generalization on cone b-metric space over Banach algebra
Huang, Huaping1 ; Radenovic, Stojan2 ; Deng, Guantie1
1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China
2 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 429-435.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.02.09
Classification : 47H10, 54H25
Keywords: Cone b-metric space over Banach algebra, fixed point, c-sequence, iterative sequence.

Huang, Huaping 1 ; Radenovic, Stojan 2 ; Deng, Guantie 1

1 School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China
2 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120, Beograd, Serbia 
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Huang, Huaping; Radenovic, Stojan; Deng, Guantie. A sharp generalization on cone b-metric space over Banach algebra. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 2, p. 429-435. doi : 10.22436/jnsa.010.02.09. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.02.09/

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