Geodesic
Cubic Functional Equations on Restricted Domains of Lebesgue Measure Zero
Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 95-103

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DOI

Let $X$ be a real normed space, $Y$ a Banach space, and $f\,:\,X\,\to \,Y$ . We prove theUlam–Hyers stability theorem for the cubic functional equation $$f\left( 2x\,+\,y \right)\,+\,f\left( 2x\,-\,y \right)\,-\,2f\left( x\,+\,y \right)\,-\,2f\left( x\,-\,y \right)\,-\,12f\left( x \right)\,=\,0$$ in restricted domains. As an application we consider a measure zero stability problem of the inequality $$\left\| f\left( 2x\,+\,y \right)\,+\,f\left( 2x\,-\,y \right)\,-\,2f\left( x\,+\,y \right)\,-\,2f\left( x\,-\,y \right)\,-\,12f\left( x \right) \right\|\,\le \,\varepsilon$$ for all $\left( x,\,y \right)$ in $\Gamma \,\subset \,{{\mathbb{R}}^{2}}$ of Lebesgue measure 0.
DOI : 10.4153/CMB-2016-041-4
Mots-clés : 39B82, Baire category theorem, cubic functional equation, first category, Lebesgue measure, Ulam-Hyers stability 
Choi, Chang-Kwon; Chung, Jaeyoung; Ju, Yumin; Rassias, John. Cubic Functional Equations on Restricted Domains of Lebesgue Measure Zero. Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 95-103. doi: 10.4153/CMB-2016-041-4
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     journal = {Canadian mathematical bulletin},
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