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''for a function $f$ defined on an interval $[a,b]$''

The greatest lower bound of constants $M>0$ in the [[Lipschitz condition|Lipschitz condition]] of order $\alpha$, $0<\alpha\leq1$,

\begin{equation*}
|f(y)-f(x)|\leq M|y-x|^{\alpha}, \quad x,y\in[a,b].
\end{equation*}


In other words, one can find
\begin{equation*}
M = \sup\limits_{x,y\in[a,b]}\frac{|f(y)-f(x)|}{|y-x|^{\alpha}}.
\end{equation*}

If $\alpha=1$ $f$ is called [[Lipschitz Function | Lipschitz function]].