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A note on stability of the popoviciu functional equation on restricted domain

Brzdęk J.

Demonstratio Mathematica

2010

Vol. 43, nr 3

635-641

We prove the Hyers-Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).

On solutions of a generalization of the Reynolds functional equation

Brzdęk J.

Demonstratio Mathematica

2008

Vol. 41, nr 4

859-868

Let (X, .) be a group endowed with a topology and F : C - X. Under some assumptions on X and F, we describe the solutions f : X - > C of the functional equation f(F(y)) . x)=f(y)f(x), that are continuous at a point or (universally, Baire, Christensen or Haar) measurable. We also show some consequences of those results.