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ON HYERS-ULAM STABILITY OF THE PEXIDER EQUATION

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