On functions behaving like additive functions |
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Authors: | J. Tabor |
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Affiliation: | (1) Dept. of Mathematics, Pedagogical University of Cracow, Podchorazych 2, Cracow, Poland |
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Abstract: | Let 0 < 1. In the paper we consider the following inequality: |f(x + y) – f(x) – f(y)| min{|f(x + y)|, |f(x) + f(y)|}, wheref: R R. Solutions and continuous solutions of this inequality are investigated. They have similar properties as additive functions, e.g. if the solution is bounded above (below) on a set of positive inner Lebesgue measure then it is continuous. Some sufficient condition for this inequality is also given.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday |
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Keywords: | Primary 39A11, 39C05 Secondary 26A99 |
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