ON HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

By Dong Zhang. Bulletin of the Australian Mathematical Society, 2015

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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.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

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