Year: 2014
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 354–362
Abstract
Let $\mathcal{G}$ be an Abelian group and let $\rho:\mathcal{G} \times \mathcal{G} \rightarrow [0, \infty)$ be a metric on $\mathcal{G}$. Let $\varepsilon$ be a normed space. We prove that under some conditions if $f:\mathcal{G}\to\varepsilon$ is an odd function and $C_x:\mathcal{G}\to\varepsilon$ defined by $C_x(y):=2f(x+y)+2f(x-y)+12f(x)-$ $f(2x+y)-f(2x-y)$ is a cubic function for all $x\in \mathcal{G},$ then there exists a cubic function $C:\mathcal{G}\to\varepsilon$ such that $f-C$ is Lipschitz. Moreover, we investigate the stability of cubic functional equation $2f(x+y)+2f(x-y)+12f(x)-f(2x+y)$ $-f(2x-y)=0$ on Lipschitz spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2014.v30.n4.2
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 354–362
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Cubic functional equation Lipschitz space stability.
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