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LOCAL Cr-RIGHT EQUIVALENCE OF Cr+1 FUNCTIONS
Published online by Cambridge University Press: 10 June 2016
Abstract
Let f,g:(ℝn, 0) → (ℝ, 0) be Cr+1 functions, r ∈ ℕ. We will show that if ∇f(0)=0 and there exist a neighbourhood U of 0 ∈ ℝn and a constant C > 0 such that
$$\begin{equation*}
\left|\partial^m(g-f)(x)\right| ≤ C \left|\nabla f(x)\right|^{r+2-|m|} \quad \textrm{ for } x\in U,
\end{equation*}
$$
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2016
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