On functions having Cauchy differences in some prescribed sets |
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| Authors: | Karol Baron Alice Simon Peter Volkmann |
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| Institution: | (1) Instytut Matematyki, Uniwersytet  laski, PL-40-007 Katowice, Poland;(2) Departement de Mathématiques, Université d'Orléans, F-45067 Orléans, France;(3) Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany |
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| Abstract: | Summary AssumeE is a real topological vector space,F is a real Banach space,K is a discrete subgroup ofF andC is a symmetric, convex and compact subset ofF such thatK  (6C) = {0}. If a functionh:E  F is continuous at at least one point andh(x + y) – h(x) – h(y)  K + C for allx, y E, then there exists a continuous linear functiona:E F such thath(x) – a(x) K + C for everyx E. |
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| Keywords: | 39B99 |
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