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January 2017 Hlawka’s functional inequality on topological groups
Włodzimierz Fechner
Banach J. Math. Anal. 11(1): 130-142 (January 2017). DOI: 10.1215/17358787-3764339


Let (X,+) be a topological abelian group. We discuss regularity of solutions f:XR of Hlawka’s functional inequality

f(x+y)+f(y+z)+f(x+z)f(x+y+z)+f(x)+f(y)+f(z), postulated for all x,y,zX. We study the lower and upper hull of f. Moreover, we provide conditions which imply continuity of f. We prove, in particular, that if X is generated by any neighborhood of zero, f is continuous at zero, and f(0)=0, then f is continuous on X.


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Włodzimierz Fechner. "Hlawka’s functional inequality on topological groups." Banach J. Math. Anal. 11 (1) 130 - 142, January 2017.


Received: 1 December 2015; Accepted: 27 February 2016; Published: January 2017
First available in Project Euclid: 30 November 2016

zbMATH: 1352.39016
MathSciNet: MR3577372
Digital Object Identifier: 10.1215/17358787-3764339

Primary: ‎39B62
Secondary: 26A15

Keywords: Drygas inequality , functional inequality , Hlawka’s inequality , subquadratic mapping

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 1 • January 2017
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