We establish some common fixed and common coincidence
point theorems for expansive type mappings in the setting of b2 metric
space. Our results extend some known results in metric spaces to b2 metric space. The research is meaningful and I recommend
it to be published when the followings have been improved.
Cite this paper
Cui, J. , Zhao, J. and Zhong, L. (2017). Unique Common Fixed Point in b2 Metric Spaces. Open Access Library Journal, 4, e3896. doi: http://dx.doi.org/10.4236/oalib.1103896.
Sahin, I. and Telci, M. (2010) A Theorem on Common Fixed Points of Expansion Type Mappings in Cone Metric Spaces. Analele Stiintifice ale Universitatii Ovidius Constanta, 18, 329-336.
Kadelburg, Z., Murthy, P.P. and Radenovic, S. (2011) Common Fixed Points for Expansive Mappings in Cone Metric Spaces. International Journal of Mathematical Analysis, 5, 1309-1319.
Shatanawi, W. and Awawde, F. (2012) Some Fixed and Coincidence Point Theorems for Expansive Maps in Cone Metric Spaces. Fixed Point Theory and Applications.
Huang, L.G. and Zhang, X. (2007) Cone Metric Spaces and Fixed Point Theorems of Contractive Mappings. Journal of Mathematical Analysis and Applications, 332, 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
Piao, Y.J. (2013) Common Fixed Points for Two Mappings Satisfying Some Expansive Conditions on 2-Metric Spaces. Journal of Systems Science and Mathematical, 33, 1370-1379.
Piao, Y.J. (2008) Unique Common Fixed Point for a Family of Self-Maps with Same Type Contractive Condition in 2-Metric Spaces. Analysis in Theory and Applications, 24, 316-320. https://doi.org/10.1007/s10496-008-0316-9
Piao, Y.J. (2012) Uniqueness of Common Fixed Point for a Family of Mappings with o-Contractive Condition in 2-Metricspaces. Applied Mathematics, 3, 73-77. https://doi.org/10.4236/am.2012.31012
Piao, Y.J. and Jin, Y.F. (2012) New Unique Common Fixed Results for Four Mappings with o-Contractive Type in 2-Metric Spaces. Applied Mathematics, 3, 734-737. https://doi.org/10.4236/am.2012.37108
Mustafa, Z., Parvaech, V., Roshan, J.R. and Kadelburg, Z. (2014) b2-Metric Spaces and Some Fixed Point Theorems. Fixed Point Theory and Applications, 144. https://doi.org/10.1186/1687-1812-2014-144
Czerwik, S. (1998) Nonlinear Set-Valued Contraction Mappings in b-Metric Spaces. Atti del Seminario Matematico e Fisico (Dell’Univ. di Modena), 46, 263-276.
Jungck, G. and Rhoades, B.E. (1998) Fixed Points for Set Valued Functions without Continuity. Indian Journal of Pure and Applied Mathematics, 29, 771-779.