A theorem of the Hahn-Banach type and its applications

Volume 57 / 1992

Zbigniew Gajda, Andrzej Smajdor, Wilhelmina Smajdor Annales Polonici Mathematici 57 (1992), 243-252 DOI: 10.4064/ap-57-3-243-252

Abstract

Let Y be a subgroup of an abelian group X and let T be a given collection of subsets of a linear space E over the rationals. Moreover, suppose that F is a subadditive set-valued function defined on X with values in T. We establish some conditions under which every additive selection of the restriction of F to Y can be extended to an additive selection of F. We also present some applications of results of this type to the stability of functional equations.

Authors

  • Zbigniew Gajda
  • Andrzej Smajdor
  • Wilhelmina Smajdor

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