Asymptotic aspect of Jensen and Jensen type functional equations in multi-normed spaces

Volume 8, Issue 4, pp 402--411 http://dx.doi.org/10.22436/jnsa.008.04.12

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Authors

Zhihua Wang - School of Science, Hubei University of Technology, Wuhan, Hubei 430068, P. R. China.

Abstract

In this paper, we investigate the Hyers-Ulam stability of additive functional equations of two forms: of ''Jensen'' and ''Jensen type'' in the framework of multi-normed spaces. We therefore provide a link between multi-normed spaces and functional equations. More precisely, we establish the Hyers-Ulam stability of functional equations of these types for mappings from Abelian groups into multi-normed spaces. We also prove the stability on a restricted domain and discuss an asymptotic behavior of functional equations of these types in the framework of multi-normed spaces.

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Keywords

• Hyers-Ulam stability
• Jensen and Jensen type functional equations
• Multi-normed spaces
• Asymptotic behavior.

MSC

•  39B52
•  58K55

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