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\begin{equation}

||f(x)||\geq g\left( \text{dist}(x,\mathcal{X})\right),

\end{equation}

with ##\mathcal{X}:= \{x:f(x)=0\}## (zero set) and some function ##g## (like a homogeneous function).

I am interested to know the class of functions. Any help will help a lot. Thanks in advance