ON THE HYERS-ULAM-RASSIAS STABILITY OF THE JENSEN EQUATION IN DISTRIBUTIONS

Title & Authors
ON THE HYERS-ULAM-RASSIAS STABILITY OF THE JENSEN EQUATION IN DISTRIBUTIONS
Lee, Eun-Gu; Chung, Jae-Young;

Abstract
We consider the Hyers-Ulam-Rassias stability problem $\small{{\parallel}2u{\circ}\frac{A}{2}-u{\circ}P_1-u{\circ}P_2{\parallel}{\leq}{\varepsilon}({\mid}x{\mid}^p+{\mid}y{\mid}^p)}$, $\small{x,y{\in}{\mathbb{R}}^n}$ for the Schwartz distributions u, which is a distributional version of the Hyers-Ulam-Rassias stability problem of the Jensen functional equation $\small{{\mid}2f(\frac{x+y}{2})-f(x)-F(y){\mid}{\leq}{\varepsilon}({\mid}x{\mid}^p+{\mid}y{\mid}^p)}$, $\small{x,y{\in}{\mathbb{R}}^n}$ for the function f : $\small{{\mathbb{R}}^n{\rightarrow}{\mathbb{C}}}$.
Keywords
stability;Gauss transforms;heat kernel;distributions;tempered distribution;Jensen functional equation;
Language
English
Cited by
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