Geodesic
Topological structures and the coincidence point of two mappings in cone b-metric spaces
Zhang, Congjun1 ; Li, Sai1 ; Liu, Baoqing1
1 School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210023, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 4, p. 1334-1344.

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

Let (X, d,K) be a cone b-metric space over a ordered Banach space ($E,\preceq$) with respect to cone P. In this paper, we study two problems: (1) We introduce a b-metric $\rho_c$ and we prove that the b-metric space induced by b-metric $\rho_c$ has the same topological structures with the cone b-metric space. (2) We prove the existence of the coincidence point of two mappings $T , f : X \rightarrow X$ satisfying a new quasi-contraction of the type $d(Tx, Ty) \preceq \Lambda\{d(fx, fy), d(fx, Ty), d(fx, Tx), d(fy, Ty), d(fy, Tx)\}$, where $\Lambda : E \rightarrow E$ is a linear positive operator and the spectral radius of $K\Lambda$ is less than 1. Our results are new and extend the recent results of [N. Hussain, M. H. Shah, Comput. Math. Appl., 62 (2011), 1677–1684], [M. Cvetković, V. Rakočević, Appl. Math. Comput., 237 (2014), 712–722], [Z. Kadelburg, S. Radenović, J. Nonlinear Sci. Appl., 3 (2010), 193–202].
DOI : 10.22436/jnsa.010.04.05
Classification : 47H10, 54H25
Keywords: Topological structures, cone b-metric spaces, quasi-contraction, points of coincidence, common fixed points.

Zhang, Congjun 1 ; Li, Sai 1 ; Liu, Baoqing 1

1 School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210023, China 
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Zhang, Congjun; Li, Sai; Liu, Baoqing. Topological structures and the coincidence point of two mappings in cone b-metric spaces. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 4, p. 1334-1344. doi : 10.22436/jnsa.010.04.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.05/

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