Quasi-additive functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1990 Germany English Publisher:Springer Science and Business Media LLCJournal:Aequationes Mathematicae, volume 39, pages 179-197 (issn: 0001-9054, eissn: 1420-8903,

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Authors: Tabor, J.;

doi: 10.1007/bf01833149

Quasi-additive functions

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Abstract

Let 0 ⩽e < 1 and letX, Y be real normed spaces. In this paper we consider the following functional inequality:∥f(x + y) − f(x) − f(y)∥ ⩽ e min{∥f(x + y)∥, ∥f(x) + f(y)∥} forx, y ∈ R, wheref: X → Y. Mainly continuous solutions are investigated. In the case whereY = R some necessary and some sufficient conditions for this inequality are given.

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Germany

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Pedagogical University
Mozambique
DigiZeitschriften
Germany

Keywords

510.mathematics, Article

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