On the stability of a mixed type functional equation in generalized functions

被引：4
作者：
Lee, Young-Su [1 ]
机构：
[1] Sogang Univ, Dept Math, Seoul 121741, South Korea
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2012年
关键词：
quadratic functional equation; additive functional equation; stability; heat kernel; Gauss transform;
D O I：
10.1186/1687-1847-2012-16
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We reformulate the following mixed type quadratic and additive functional equation with n-independent variables as the equation for the spaces of generalized functions. Using the fundamental solution of the heat equation, we solve the general solution and prove the Hyers-Ulam stability of this equation in the spaces of tempered distributions and Fourier hyperfunctions. Mathematics Subject Classification 2000: 39B82; 39B52.
引用
收藏
页码：1 / 11
页数：11
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