On the characterization of compactness in the space of functions of bounded variation in the sense of Jordan

Dariusz Bugajewski , Jacek Gulgowski

Abstract

The main goal of this paper is to prove a compactness criterion for subsets of the Banach space of functions of bounded variation in the sense of Jordan. In comparison to the compactness criterion contained in Dunford–Schwartz’s monograph, the conditions which appear in our criterion seems to be easier to verify. Moreover, using this criterion we define a quasimeasure of noncompactness in that space. Some applications of quasimeasures of noncompactness to fixed point theorems are also presented.
Author Dariusz Bugajewski
Dariusz Bugajewski,,
-
, Jacek Gulgowski (FMPI/IM)
Jacek Gulgowski,,
- Institute of Mathematics
Journal seriesJournal of Mathematical Analysis and Applications, ISSN 0022-247X, e-ISSN 1096-0813, (N/A 70 pkt)
Issue year2020
Vol484
No2
Pages1-17
Publication size in sheets6187.60
Article number123752
Keywords in Englishcompact set, functions of boundedvariation, quasimeasure of noncompactness, variation in the sense of Jordan
ASJC Classification2603 Analysis; 2604 Applied Mathematics
DOIDOI:10.1016/j.jmaa.2019.123752
Languageen angielski
LicenseRepository; published final; Uznanie Autorstwa - Użycie Niekomercyjne - Bez utworów zależnych (CC-BY-NC-ND); with publication
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Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 02-06-2020, ArticleFromJournal
Publication indicators WoS Citations = 0.000; Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.187; WoS Impact Factor: 2018 = 1.188 (2) - 2018=1.219 (5)
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LicencjaUtwór jest udostępniany na licencji Creative Commons Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 4.0 Międzynarodowe (CC BY-NC-ND 4.0) https://creativecommons.org/licenses/by-nc-nd/4.0/
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* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
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