Some Remarks on Generalized Metric Spaces of Branciari
DOI:
https://doi.org/10.5644/SJM.10.2.07Keywords:
Generalized metric space, fixed pointAbstract
In this paper, we prove some properties of a generalized metric space in the sense of Branciari. As applications, we correct some confusion about this space in the literature. Examples are given to illustrate the results.
2010 Mathematics Subject Classification. Primary 46A16, 54H25; Secondary 54D99, 54E99
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References
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (1–2) (2000), 31–37.
P. Das, A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sci., 1 (2002), 29–33.
P. Das and L. K. Dey, A fixed point theorem in a generalized metric space, Soochow J. Math., 33 (2007), 33–29.
P. Das and L. K. Dey, Fixed point of contractive mappings in generalized metric spaces, Math. Slovaca, 59 (4) (2009), 499–504.
P. Das and L. K. Dey, Porosity of certain classes of operators in generalized metric spaces, Demonstratio Math., XLII (1) (2009), 163–174.
R. Engelking, General Topology, Sigma series in pure mathematics, vol. 6, Heldermann Verlag, Berlin, 1988.
I. M. Erhan, E. Karapinar, and T. Sekulic, Fixed points of (ψ, φ) contractions on generalized metric spaces, Fixed Point Theory Appl., 2012:138 (2012), 1–10.
S. P. Franklin, Spaces in which sequences suffice, Fund. Math., 57 (1965), 107–115.
L. Kikina and K. Kikina, On fixed point of a Ljubomir Ciric quasi-contraction mapping in generalized metric spaces, Publ. Math. Debrecen, 83 (3) (2013), 1–6.
L. Kikina and K. Kikina, A fixed point theorem in generalized metric spaces, Demonstratio Math., XLVI (1) (2013), 181–190.
W. A. Kirk and N. Shahzad, Generalized metrics and Caristi’s theorem, Fixed Point Theory Appl., 2013:129 (2013), 1–9.
B. K. Lahiri and P. Das, Fixed point of a Ljubomir Ciric’s quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen, 61 (3–4) (2002), 589–594.
B. Samet, Discussion on “A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces” by A. Branciari, Publ. Math. Debrecen, 76 (4) (2010), 493–494.
H. Lakzian B. Samet, Fixed points for (ψ, ϕ)-weakly contractive mappings in generalized metric spaces, Appl. Math. Lett., 25 (2012), 902–906.
I. R. Sarma, J. M. Rao, and S. S. Rao, Contractions over generalized metric spaces, J. Nonlinear Sci. Appl., 2 (3) (2009), 180–182.
M. Turinici, Functional contractions in local Branciari metric spaces, ROMAI J., 8 (2) (2012), 189–199.