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http://dx.doi.org/10.5831/HMJ.2011.33.4.467

ON THE STABILITY OF THE PEXIDER EQUATION IN SCHWARTZ DISTRIBUTIONS VIA HEAT KERNEL  

Chung, Jae-Young (Department of Mathematics, Kunsan National University)
Chang, Jeong-Wook (Department of Mathematics Education, Dankook University)
Publication Information
Honam Mathematical Journal / v.33, no.4, 2011 , pp. 467-485 More about this Journal
Abstract
We consider the Hyers-Ulam-Rassias stability problem $${\parallel}u{\circ}A-{\upsilon}{\circ}P_1-w{\circ}P_2{\parallel}{\leq}{\varepsilon}({\mid}x{\mid}^p+{\mid}y{\mid}^p)$$ for the Schwartz distributions u, ${\upsilon}$, w, which is a distributional version of the Pexider generalization of the Hyers-Ulam-Rassias stability problem ${\mid}(x+y)-g(x)-h(y){\mid}{\leq}{\varepsilon}({\mid}x{\mid}^p+{\mid}y{\mid}^p)$, x, $y{\in}\mathbb{R}^n$, for the functions f, g, h : $\mathbb{R}^n{\rightarrow}\mathbb{C}$.
Keywords
Stability; Gauss transforms; heat kernel; distributions; tempered distribution; Cauchy equation; Pexider equation;
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