Stability of quadratic functional equations in tempered distributions

被引：2
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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