On Hyers-Ulam stability of the Pexider equation

Abstract

Let (S, +) be a commutative semigroup and let X be a sequentially complete linear topological Hausdorff space. In the theory of functional equations the problem of the stability (in a sense) has been considered by many authors. We recall only two results concerning the stability of the Pexider equation. In [1] E. Glowacki and Z. Kominek have proved that under the above assumptions, for arbitrary functions f,g,h : S —• X fulfilling the condition (Fragment tekstu).