On Pexider Differences in Topological Vector Spaces

Abstract EN

Let X be a normed space and Y a sequentially complete Hausdorff topological vector space over the field Q of rational numbers.

Let D1={(x,y)∈X×X:∥x∥+∥y∥≥d}, and D2={(x,y)∈X×X:∥x∥+∥y∥0.

We prove that the Pexiderized Jensen functional equation is stable for functions defined on D1(D2), and taking values in Y.

We consider also the Pexiderized Cauchy functional equation.