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ON HYPERSTABILITY OF GENERALISED LINEAR FUNCTIONAL EQUATIONS IN SEVERAL VARIABLES

Published online by Cambridge University Press:  02 June 2015

DONG ZHANG
DONG ZHANG*
Affiliation:
LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, PR China email dongzhang@pku.edu.cn
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Abstract

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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.

Keywords

linear functional equation with multiple variablesapproximate solutionfixed pointCauchy equationFréchet equationJordan–von Neumann functional equation

MSC classification

Primary: 39B82: Stability, separation, extension, and related topics
Secondary: 39B52: Equations for functions with more general domains and/or ranges 39B62: Functional inequalities, including subadditivity, convexity, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 259 - 267
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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