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The sum of coefficients of bounded univalent functions

Authors:	D V Prokhorov

Institution:	(1) N. G. Chernyshevskii Saratov State University, Saratov, USSR

Abstract:	We solve the maximal value problem for the functional $\operatorname{Re} \sum\nolimits_{j = 1}^m {a_{k_j } }$ in the class of functionsf(z)=z+a ₂z²+… that are holomorphic and univalent in the unit disk and satisfy the inequality \|f(z)\|<M. We prove that the Pick functions are extremal for this problem for sufficiently largeM whenever the set of indicesk ₁,…,k_m contains an even number. Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 728–733, May, 1997. Translated by S. S. Anisov

Keywords:	holomorphic functions Pick functions Koebe functions maximal value problem
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