On Pexider differences in topological vector spaces (Q657117)

Summary: Let \(X\) be a normed space and \(Y\) a sequentially complete Hausdorff topological vector space over the field \(\mathbb Q\) of rational numbers. Let \(D_1 = \{(x, y) \in X \times X : {\|}x{\|} + {\|}y{\|} \geq d\}\), and \(D_2 = \{(x, y) \in X \times X : {\|}x{\|} + {\|}y{\|} < d\}\) where \(d > 0\). We prove that the Pexiderized Jensen functional equation is stable for functions defined on \(D_1\) \((D_2)\), and taking values in \(Y\). We consider also the Pexiderized Cauchy functional equation.