On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation

Dariusz Bugajewski , Jacek Gulgowski , Piotr Kasprzak

Abstract

In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded variation, namely the problem concerning their continuity. We basically consider autonomous superposition operators generated by analytic functions or functions of C1-class. We also investigate the problem of compactness of some classical linear and nonlinear operators acting in the space of functions of bounded variation in the sense of Jordan. We apply our results to the examination of the existence and the topological properties of solutions to nonlinear equations in those spaces.
Author Dariusz Bugajewski
Dariusz Bugajewski,,
-
, Jacek Gulgowski (FMPI / IM)
Jacek Gulgowski,,
- Institute of Mathematics
, Piotr Kasprzak
Piotr Kasprzak,,
-
Journal seriesAnnali di Matematica Pura Ed Applicata, ISSN 0373-3114, (A 30 pkt)
Issue year2016
Vol195
No5
Pages1513-1530
Publication size in sheets0.85
Keywords in Englishacting condition, aronszajn-type theorem, autonomous (nonautonomous) superposition operator, Bernstein polynomials, compact operator, hammerstein integral equation, linear integral operator, locally bounded mapping, modulus of continuity, p-variation, positive solution, Rδ-set, variation in the sense of Jordan, Volterra-Hammerstein integral equation, φ-function, φ-variation
DOIDOI:10.1007/s10231-015-0526-7
URL http://link.springer.com/article/10.1007%2Fs10231-015-0526-7
Languageen angielski
LicenseOther; published final; Uznanie Autorstwa (CC-BY); with publication
Score (nominal)35
ScoreMinisterial score = 30.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 35.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 0.864 (2) - 2016=0.968 (5)
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