%0 Journal Article %T Topological structures and the coincidence point of two mappings in cone b-metric spaces %A Zhang, Congjun %A Li, Sai %A Liu, Baoqing %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 4 %@ ISSN 2008-1901 %F Zhang2017 %X 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]. %9 journal article %R 10.22436/jnsa.010.04.05 %U http://dx.doi.org/10.22436/jnsa.010.04.05 %P 1334--1344 %0 Journal Article %T Common fixed point results for noncommuting mappings without continuity in cone metric spaces %A M. Abbas %A G. Jungck %J J. Math. Anal. Appl. %D 2008 %V 341 %F Abbas2008 %0 Book %T Cones and duality %A C. D. Aliprantis %A R. Tourky %D 2007 %I Graduate Studies in Mathematics, American Mathematical Society, Providence %C RI %F Aliprantis2007 %0 Journal Article %T On an equivalence of topological vector space valued cone metric spaces and metric spaces %A H. Çakallı %A A. Sönmez %A Ç . Genç %J Appl. Math. Lett. %D 2012 %V 25 %F Çakallı2012 %0 Journal Article %T Quasi-contraction of Perov type %A M. Cvetković %A V. Rakočević %J Appl. Math. Comput. %D 2014 %V 237 %F Cvetković2014 %0 Journal Article %T Nonlinear set-valued contraction mappings in b-metric spaces %A S. Czerwik %J Atti Sem. Mat. Fis. Univ. Modena %D 1998 %V 46 %F Czerwik1998 %0 Journal Article %T Cone metric spaces and fixed point theorems of contractive mappings %A L.-G. Huang %A X. Zhang %J J. Math. Anal. Appl. %D 2007 %V 332 %F Huang2007 %0 Journal Article %T KKM mappings in cone b-metric spaces %A N. Hussain %A M. H. Shah %J Comput. Math. Appl. %D 2011 %V 62 %F Hussain2011 %0 Journal Article %T Cantor’s intersection theorem for K-metric spaces with a solid cone and a contraction principle %A J. Jachymski %A J. Klima %J J. Fixed Point Theory Appl. %D 2016 %V 18 %F Jachymski2016 %0 Journal Article %T Commuting mappings and fixed points %A G. Jungck %J Amer. Math. Monthly %D 1976 %V 83 %F Jungck1976 %0 Journal Article %T Some common fixed point results in non-normal cone metric spaces %A Z. Kadelburg %A S. Radenović %J J. Nonlinear Sci. Appl. %D 2010 %V 3 %F Kadelburg2010 %0 Journal Article %T KKM mappings in metric type spaces %A M. A. Khamsi %A N. Hussain %J Nonlinear Anal. %D 2010 %V 73 %F Khamsi2010 %0 Journal Article %T New common fixed point theorems for maps on cone metric spaces %A G.-X. Song %A X.-Y. Sun %A Y. Zhao %A G.-T. Wang %J Appl. Math. Lett. %D 2010 %V 23 %F Song2010