Aequationes mathematicae

, Volume 85, Issue 1, pp 111–118

The properties of functional inclusions and Hyers–Ulam stability

Open AccessArticle

DOI: 10.1007/s00010-012-0119-0

Cite this article as:
Piszczek, M. Aequat. Math. (2013) 85: 111. doi:10.1007/s00010-012-0119-0

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 
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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of MathematicsPedagogical UniversityKrakówPoland