Stability of the Cauchy congruence on restricted domain期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Stability of the Cauchy congruence on restricted domain

Authors:	Email author" target="_blank">J?Brzdek Email author Email author" target="_blank">J?Tabor Email author

Institution:	(1) Department of Mathematics, Pedagogical University, Podchorazych 2, PL-30-084 Kraków, Poland;(2) Department of Mathematics, University of Rzeszów, Rejtana 16 A, PL-35-310 Rzeszów, Poland

Abstract:	Let S be a real interval with $0 \in S,\, \varepsilon \in (0, {1 \over 4})$ , and $h : S \rightarrow \mathbb{R}$ be a function satisfying $h(x + y) - h(x) - h(y) \in \mathbb{Z} + -\varepsilon, \varepsilon] \quad \textrm{for}\,\, x,\, y \in S\,\, \textrm{with}\,\, x + y \in S.$ We show that if h is Lebesgue or Baire measurable, then there exists $c \in \mathbb{R}$ such that $h(x) - cx \in \mathbb{Z} + -\varepsilon, \varepsilon]\quad \textrm{for}\, x \in S.$ That result is motivated by a question of E. Manstaviius. Received: 11 February 2003

Keywords:	39B22
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