Cubic Functional Equations on Restricted Domains of Lebesgue Measure Zero

Canadian mathematical bulletin

John Rassias¹  Yumin Ju²  Jaeyoung Chung²  Chang-Kwon Choi³ 

[1] National and Capodistrian University of Athens, Pedagogical Department E. E., Athens, Greece;Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea;Department of Mathematics, Jeonbuk National University, Jeonju 561-756, Republic of Korea

关键词: Baire category theorem;    cubic functional equation;    first category;    Lebesgue measure;    Ulam-Hyers stability;   

DOI  :  10.4153/CMB-2016-041-4

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $X$ be a real normed space, $Y$ a Bancch space and $f:X oY$.We prove the Ulam-Hyers stability theoremfor the cubic functional equationegin{align*}f(2x+y)+f(2x-y)-2f(x+y)-2f(x-y)-12f(x)=0end{align*}in restricted domains. As an application we consider a measurezero stability problemof the inequalityegin{align*}|f(2x+y)+f(2x-y)-2f(x+y)-2f(x-y)-12f(x)|le epsilonend{align*}for all $(x, y)$ in $Gammasubsetmathbb R^2$ of Lebesgue measure0.

【 授权许可】

Unknown