On the continuity of superposition operators in the space of functions of bounded variation

Piotr Maćkowiak


In the paper we present results on the continuity of nonlinear superposition operators acting in the space of functions of bounded variation in the sense of Jordan. It is shown that the continuity of an autonomous superposition operator is automatically guaranteed if the acting condition is met. We also give a simple proof of the fact that a nonautonomous superposition operator generated by a continuously differentiable function is uniformly continuous on bounded sets. Moreover, we present necessary and sufficient conditions for the continuity of a superposition operator (autonomous or nonautonomous) in a general setting. Thus, we give the answers to two basic open problems mentioned in the monograph (Appell et al. in Bounded variation and around, series in nonlinear analysis and application, De Gruyter, Berlin, 2014).
Author Piotr Maćkowiak (WIiGE / KEM)
Piotr Maćkowiak,,
- Department of Mathematical Economics
Journal seriesAequationes Mathematicae, ISSN 0001-9054, (A 25 pkt)
Issue year2017
Publication size in sheets0.9
Keywords in EnglishAutonomous superposition operator Continuity of superposition operator Function of bounded variation in the sense of Jordan Nonautonomous superposition operator
ASJC Classification2600 General Mathematics; 2604 Applied Mathematics; 2607 Discrete Mathematics and Combinatorics
URL https://link.springer.com/content/pdf/10.1007%2Fs00010-017-0491-x.pdf
Languageen angielski
Score (nominal)25
Score sourcejournalList
ScoreMinisterial score = 25.0, 12-03-2020, ArticleFromJournal
Publication indicators WoS Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2017 = 1.109; WoS Impact Factor: 2017 = 0.644 (2) - 2017=0.685 (5)
Citation count*4 (2020-09-16)
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