Topological structures and the coincidence point of two mappings in cone b-metric spaces


Authors

Congjun Zhang - School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210023, China. Sai Li - School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210023, China. Baoqing Liu - School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing, Jiangsu, 210023, China.


Abstract

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].


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ISRP Style

Congjun Zhang, Sai Li, Baoqing Liu, Topological structures and the coincidence point of two mappings in cone b-metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1334--1344

AMA Style

Zhang Congjun, Li Sai, Liu Baoqing, Topological structures and the coincidence point of two mappings in cone b-metric spaces. J. Nonlinear Sci. Appl. (2017); 10(4):1334--1344

Chicago/Turabian Style

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 Applications, 10, no. 4 (2017): 1334--1344


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