ON HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

Abstract

We obtain some results on approximate solutions of the generalised linear functional equation $\sum _{i=1}^{m}L_{i}f(\sum _{j=1}^{n}a_{ij}x_{j})=0$ for functions mapping a normed space into a normed space. We show that, under suitable assumptions, the approximate solutions are in fact exact solutions. The theorems correspond to and complement recent results on the hyperstability of generalised linear functional equations.