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On the metrizability of cone metric spaces. (English) Zbl 1206.54026

Summary: We show in this paper that a (complete) cone metric space \((X,E,P,d)\) is indeed (completely) metrizable for a suitable metric \(D\). Moreover, given any finite number of contractions \(f_{1},\dots ,f_n\) on the cone metric space \((X,E,P,d), D\) can be defined in such a way that these functions become also contractions on \((X,D)\).

MSC:

54E35 Metric spaces, metrizability
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References:

[1] Amini-Harandi, A.; Fakhar, M., Fixed point theory in cone metric spaces obtained via the scalarization method, Computers and Mathematics with Applications, 59, 11, 3529-3534 (2010) · Zbl 1197.54055
[2] Z. Kadelburg, S. Radenovic, V. Rakocevic, A note on equivalence of some metric and cone metric fixed point results, Applied Mathematics Letters, doi:10.1016/j.aml.2010.10.030; Z. Kadelburg, S. Radenovic, V. Rakocevic, A note on equivalence of some metric and cone metric fixed point results, Applied Mathematics Letters, doi:10.1016/j.aml.2010.10.030 · Zbl 1213.54067
[3] Huang, L.-G.; Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings, Journal of Mathematical Analysis and Applications, 332, 1468-1476 (2007) · Zbl 1118.54022
[4] Raja, P.; Vaezpour, S. M., Some extensions of Banach’s fixed point theorem in complete cone metric spaces, Journal of Fixed Point Theory and Applications, 1-11 (2008) · Zbl 1148.54339
[5] Rezapour, Sh.; Hamlbarani, R., Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, Journal of Mathematical Analysis and Applications, 345, 2, 719-724 (2008) · Zbl 1145.54045
[6] Du, W. S., A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis TMA, 72, 2259-2261 (2010) · Zbl 1205.54040
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