The problem of isoperimetric distortion for univalent Montel functions (Q1358089)

Denote by \(M(a)\) the class of all functions analytic and univalent in the unit disk, and satisfying the conditions \(f(0)=0\), \(f(a)=a\) for a fixed \(a\), \(0<a<1\). In this paper the problem of determining best bounds of \(|f'(a) |\) for fixed \(|f'(0) |\) and \(f\) in \(M(a)\) is solved. The solution is based on the method of extremal length and on results due to \textit{G. V. Kuzmina} Tr. Mat. Inst. Steklova 139, 1-240 (1980; Zbl 0482.30015)].