Abstract
The notion of almost convexity is studied and an extension of Kuczma’s theorem, originally proved in finite-dimensional spaces, is presented. The phrase “almost” is meant in the sense of abstract σ-ideals. The main result also generalizes the theorem proved in Jarczyk and Laczkovich (Math Inequal Appl 13:217–225, 2009).
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To Professor János Aczél on the occasion of his 85th birthday
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Jarczyk, W. Almost convexity on Abelian groups. Aequat. Math. 80, 141–154 (2010). https://doi.org/10.1007/s00010-010-0044-z
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DOI: https://doi.org/10.1007/s00010-010-0044-z