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Title: Hlawka's functional inequality
Authors: Fechner, Włodzimierz
Keywords: Functional inequality; Hlawka’s inequality; Popoviciu’s inequality; sublinear mapping; additive mapping; linear mapping; quadratic mapping; Dini derivative; quadrilateral space; Hlawka space
Issue Date: 2014
Citation: Aequationes Mathematicae, Vol. 87, no. 1/2 (2014), s. 71-87
Abstract: The paper is devoted to the functional inequality (called by us Hlawka’s functional inequality) f(x + y) + f(y + z) + f(x + z) ≤ f(x + y + z) + f(x) + f(y) + f(z) for the unknown mapping f defined on an Abelian group, on a linear space or on the real line. The study of the foregoing inequality is motivated by Hlawka’s inequality: x + y + y + z + x + z ≤ x + y + z + x + y + z , which in particular holds true for all x, y, z from a real or complex inner product space.
DOI: 10.1007/s00010-012-0178-2
ISSN: 0001-9054
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