Some results on extended b-metric spaces and Pompeiu-Hausdorff metric.

Ledia Subashi, Nertila Gjini

Abstract


In this paper we will show some new results about extended b- metric space. Given an extended b-metric space  (X,d),we may define a new extended b- metric space with Pompeiu- Hausdorff metric H on the set H(X) of the collection of all nonempty compact subsets of X. We will show that if is a complete extended b- metric space then the Hausdorff extended b-metric space (H(X),H) is also complete.


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References


T. Kamran, M. Samreen, Q. UL Ain (2017). A generalization of b-metric space and some fixed point theorems. MDPI Mathematics Journal, 5 ,19, 2017 doi:10.3390/math5020019

Subashi, L. (2017). Some topological properties of extended b-metric space, Proceedings of The 5th International Virtual Conference on Advanced Scientific Results (SCIECONF-2017), Vol. 5, pg 164-167. Zilina, Slovakia. doi: 10.18638/scieconf.2017.5.1.451

Bourbaki, N. (1974) Topologie Generale; Herman: Paris, France, 1974.

Czerwik, S. (1993). Contraction mappings in b-metric spaces. (pp 5–11). Acta Math. Inform. Univ. Ostra. 1.

D. Pompeiu (1905). Sur la continuite' des fonctions de variables complexes (These). Gauthier- Villars, Paris, ;Ann.Fac.Sci.deToulouse 7:264-315.

F. Hausdorff (1914). Grunclzuege der Mengenlehre. Viet, Leipzig.

https://www.math.wisc.edu/~seeger/522/c13.pdf


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