Approximation of the Cubic Functional Equations in Lipschitz Spaces
Year: 2014
Analysis in Theory and Applications, Vol. 30 (2014), Iss. 4 : pp. 354–362
Abstract
Let G be an Abelian group and let ρ:G×G→[0,∞) be a metric on G. Let ε be a normed space. We prove that under some conditions if f:G→ε is an odd function and Cx:G→ε defined by Cx(y):=2f(x+y)+2f(x−y)+12f(x)− f(2x+y)−f(2x−y) is a cubic function for all x∈G, then there exists a cubic function C:G→ε 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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