Stability of quadratic functional equations in tempered distributions

被引：1

作者：

Lee, Young-Su ^{[1
]}

机构：

[1] Sogang Univ, Dept Math, Seoul 121741, South Korea

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2012年

关键词：

quadratic functional equation; stability; tempered distribution; heat kernel; Gauss transform; ULAM-RASSIAS STABILITY; SPACES;

D O I：

10.1186/1029-242X-2012-177

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We reformulate the following quadratic functional equation: f(kx + y) + f(kx - y) = 2k(2)f(x) + 2f(y) as the equation for generalized functions. Using the fundamental solution of the heat equation, we solve the general solution of this equation and prove the Hyers-Ulam stability in the spaces of tempered distributions and Fourier hyperfunctions.

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页数：11

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