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On Hyers-Ulam stability of the Pexider equation

Kominek Z.

Demonstratio Mathematica

2004

Vol. 37, nr 2

373--376

Abstract Boundedness and the Stability of the Pexider Equation

Ger R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2003

Vol. 9

41--49

Let (S, +) be a semigroup (not necessarily Abelian) and let (X,+) be a commutative group. We deal with an axiomatically given family B ⸦ 2x of "bounded sets" and with mappings f, g, h : S → X such that the transformation S x S ∋ (x, y) → f (x + y) - g (x) - h (y) ∈ X remains B-bounded. Stability results existing in the literature in connection with the Pexider functional equation become special cases of our theorems up to the magnitude of approximating constants.