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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On subadditive functions

Authors: Janusz Matkowski and Tadeusz Świątkowski
Journal: Proc. Amer. Math. Soc. 119 (1993), 187-197
MSC: Primary 26A15; Secondary 39B72
MathSciNet review: 1176072
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Abstract: The main result says that every one-to-one subadditive function $ f:(0,\infty ) \to (0,\infty )$ such that $ {\lim _{t \to 0}}f(t) = 0$ must be continuous everywhere. A construction of a broad class of discontinuous subadditive bijections of $ (0,\infty )$ which are bounded in every vicinity of 0 is given. Moreover, a problem of extension of a subadditive function defined in $ (0,\infty )$ to a subadditive even function in $ \mathbb{R}$ is considered

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Keywords: One-to-one subadditive functions in $ (0,\infty )$, subadditive bijections of $ {\mathbb{R}_ + }$, even subadditive functions in $ \mathbb{R}$
Article copyright: © Copyright 1993 American Mathematical Society

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