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Aequationes mathematicae

, Volume 85, Issue 1–2, pp 111–118 | Cite as

The properties of functional inclusions and Hyers–Ulam stability

  • Magdalena Piszczek
Open Access
Article

Abstract

We prove that a set-valued function satisfying some functional inclusions admits, in appropriate conditions, a unique selection satisfying the corresponding functional equation. As a consequence we obtain the result on the Hyers–Ulam stability of that functional equation.

Mathematics Subject Classification (2010)

39B05 39B82 54C60 54C65 

Keywords

Stability of functional equation set-valued map selection 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of MathematicsPedagogical UniversityKrakówPoland

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