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Approximation of the Cubic Functional Equations in Lipschitz Spaces
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Let G be an Abelian group and letρ:G×G→[0,∞) be a metric on G. Let E be a normed space. We prove that under some conditions if f:G→E is an odd function and Cx:G→E defined by Cx(y):=2 f (x+y)+2 f (x?y)+12 f (x)?f (2x+y)?f (2x?y) is a cubic function for all x∈G, then there exists a cubic function C:G→E such that f?C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2 f (x+y)+2 f (x?y)+12 f (x)?f (2x+y)?f (2x?y)=0 on Lipschitz spaces.
Cubic functional equationLipschitz spacestability
A Ebadian、N Ghobadipour、I Nikoufar、and M Eshaghi Gordji
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Department of Mathematics, Payame Noor University, Iran
Department of Mathematics, Urmia University, Urmia, Iran
Department of Mathematics, Semnan University, P. 0. Box 35195-363, Semnan, Iran
NETL
NSTL
万方数据
维普
