Article

Aequationes mathematicae

, Volume 85, Issue 1, pp 111-118

Open Access This content is freely available online to anyone, anywhere at any time.

The properties of functional inclusions and Hyers–Ulam stability

  • Magdalena PiszczekAffiliated withInstitute of Mathematics, Pedagogical University Email author 

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