A fixed point theorem in \(S_b\)-metric spaces
- Department of Natural Sciences, Community College of Riyadh, King Saud University, Riyadh, Saudi Arabia.
- Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
In this paper, we introduce an interesting extension of the \(S\)-metric spaces called \(S_b\)-metric spaces,
in which we show the existence of fixed point for a self mapping defined on such spaces. We also
prove some results on the topology of the \(S_b\)-metric spaces.
- Functional analysis
- \(S_b\)-metric space
- common fixed point.
H. Aydi, M.-F. Bota, E. Karapnar, S. Mitrovi, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl., 2012 (2012 ), 8 pages.
I. A. Bakhtin, The contraction mapping principle in almost metric space, Functional Analysis, Ulianowsk. Gos. Ped. Ins., 30 (1989), 26-37.
V. Berinde , Iterative Approximation of Fixed points, Springer, Berlin (2007)
M. Bota, A. Molnar, C. Varga, On Ekeland's variational principle in b-metric spaces, Fixed Point Theory, 12 (2011), 21-28.
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11.
A. K. Dubey, R. Shukla, R. P. Dubey, Some fixed point results in b-metric spaces , Asian J. Math. Appl., 2014 (2014 ), 6 pages.
M. Kir, H. Kiziltunc, On Some Well Known Fixed Point Theorems in b-Metric Spaces, Turkish J. Anal. Number Theory, 1 (2013), 13-16.
M. Mlaiki, Common fixed points in complex S-metric space, Adv. Fixed Point Theory, 4 (2014), 509-524.
N. Mlaiki, \(\alpha-\psi\)-Contractive Mapping on S-Metric Space, Math. Sci. Lett., 4 (2015), 9-12.
A. Mukheimer, \(\alpha-\psi-\phi\)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 168-179.
K. Prudhvi, Fixed Point Theorems in S-Metric Spaces, Univer. J. Comput. Math., 3 (2015), 19-21.
S. Sedghi, N. Shobe, A Common unique random fixed point theorems in S-metric spaces, J. Prime Res. Math., 7 (2011), 25-34.
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik , 64 (2012), 258-266.
S. Sedghi, N. Van Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik , 66 (2014), 113-124.
W. Shatanawi, Fixed Point Theory for Contractive Mappings Satisfying \(\Phi\)-Maps in G-Metric Spaces, Fixed Point Theory Appl., 2010 (2010 ), 9 pages.
W. Shatanawi, E. Karapinar, H. Aydi, Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with a c-Distance, J. Appl. Math., 2012 (2012 ), 15 pages.
W. Shatanawi, A. Pitea, Some coupled fixed point theorems in quasi-partial metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 15 pages.
C.Vetro, S. Chauhan, E. Karapinar, W. Shatanawi, Fixed Points of Weakly Compatible Mappings Satisfying Generalized \(\varphi\)-Weak Contractions, Bull. Malays. Math. Sci. Soc., 38 (2015), 1085-1105.
S. Shukla, Partial b-Metric Spaces and Fixed Point Theorems, Mediterr. J. math., 11 (2014), 703-711.
A. Singh, N. Hooda, Coupled Fixed Point Theorems in S-metric Spaces, Inter. J. Math. Stat. Invent., 2 (2014), 33-39.