Lipschitz constant

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

The greatest lower bound of constants $M>0$ in the 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.