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

Volume 10, Issue 2, pp 429--435 http://dx.doi.org/10.22436/jnsa.010.02.09

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.

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ISRP Style

Huaping Huang, Stojan Radenovic, Guantie Deng, A sharp generalization on cone b-metric space over Banach algebra, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 2, 429--435

AMA Style

Huang Huaping, Radenovic Stojan, Deng Guantie, A sharp generalization on cone b-metric space over Banach algebra. J. Nonlinear Sci. Appl. (2017); 10(2):429--435

Chicago/Turabian Style

Huang, Huaping, Radenovic, Stojan, Deng, Guantie. "A sharp generalization on cone b-metric space over Banach algebra." Journal of Nonlinear Sciences and Applications, 10, no. 2 (2017): 429--435

Keywords

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

MSC

47H10
54H25

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