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2021, vol. 25, br. 1, str. 63-69
Measures of noncompactness on w-distance spaces
(naslov ne postoji na srpskom)
Univerzitet u Nišu, Prirodno-matematički fakultet

e-adresaakos2804@gmail.com
Projekat:
Ministarstvo prosvete, nauke i tehnološkog razvoja Republike Srbije (institucija: Univerzitet u Nišu, Prirodno-matematički fakultet) (MPNTR - 451-03-68/2020-14/200124)

Ključne reči: Measures of noncompactness; metric spaces; w-distance
Sažetak
(ne postoji na srpskom)
The aim of this paper is to provide a new framework for the study of measures of noncompactness in generalized metric spaces. Firstly, we introduce the notion of w-measure of noncompactness on metric spaces with a w-distance and extend the diameter and Kuratowski functionals to this setting. At the end we give a characterization of metric completeness via our main results, providing a new answer to the open question mentioned by Arandjelović in his PhD thesis [2].
Reference
Arandjelović, I. (1999) Stavovi o presecanju i njihove primene u nelinearnoj analizi. University of Belgrade-Faculty of Mathematics, (in Serbian), PhD thesis
Arandjelović, I.D. (1998) Measures of noncompactness on uniform spaces. Mathematica Moravica, 2: 1-8
Banaś, J., Mursaleen, M. (2014) Sequence spaces and measures of noncompactness with applications to differential and integral equations. Springer
Darbo, G. (1955) Punti uniti in transformazoioni a codminio noncompactto. Rendiconti del Seminario Matematico della Università di Padova, 24, 84-92
Ilić, D., Rakočević, V. (2008) Common fixed points for maps on metric space with w-distance. Applied Mathematics and Computation, 199(2): 599-610
Kada, O., Suzuki, T., Takahashi, W. (1996) Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Mathematica Japonica, 44, 381-391
Kostić, A. (2019) Best proximity points revisited. Filomat, 33(16): 5159-5166
Kostić, A., Karapinar, E., Rakočević, V. (2019) Best proximity points and fixed points with Rfunctions in the framework of w-distances. Bulletin of the Australian Mathematical Society, 99(03): 497-507
Kostić, A., Rakočević, V., Radenović, S. (2019) Best proximity points involving simulation functions with w0-distance. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales: Serie A. Matemáticas, 113(2): 715-727
Kuratowski, K. (1930) Sur les espaces complets. Fundamenta Mathematicae, 15: 301-309
Malkowsky, E., Rakočević, V. (2000) An introduction into the theory of sequence spaces and measures of noncompactness. Zbornik radova Matematičkog instituta SANU, 9(17), 143-234
Manoranjan, S., Koushik, S. (2017) Towards cantor intersection theorem and Baire category theorem in partial metric spaces. Matematički vesnik, vol. 69, br. 2, str. 126-132
Rakočević, V. (1998) Measures of noncompactness and some applications. Filomat, 12(2): 87-120
Suzuki, T., Takahashi, W. (1996) Fixed point theorems and characterizations of metric completeness. Topological Methods in Nonlinear Analysis, 8(2): 371-382
 

O članku

jezik rada: engleski
vrsta rada: neklasifikovan
DOI: 10.5937/MatMor2101063K
primljen: 13.05.2020.
revidiran: 02.10.2020.
prihvaćen: 30.11.2020.
objavljen onlajn: 16.03.2021.
objavljen u SCIndeksu: 16.04.2021.
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