Nonlinear version of Holub's theorem and its application (Q5955844)

The authors prove the formula \[ 1+ L(f)= \max\{L(I+ f), L(I- f)\} \] for the smallest Lipschitz constant \(L(f)\) of a Lipschitz continuous operator \(f\) in a Banach space. Moreover, they discuss a connection with the so-called Dahlquist constant \[ M(f)= \lim_{\varepsilon\to 0+} {L(f+\varepsilon f)-1\over \varepsilon} \] of \(f\) which in turn allows invertibility results for \(f\).