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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 1997 Volume 61, Issue 5, Pages 728–733 (Mi mzm1554)

This article is cited in 1 paper

The sum of coefficients of bounded univalent functions

D. V. Prokhorov

Saratov State University named after N. G. Chernyshevsky

Abstract: We solve the maximal value problem for the functional $\operatorname{Re}\sum_{j=1}^ma_{k_j}$ in the class of functions $f(z)=z+a_2z^2+\dotsb$ 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 large $M$ whenever the set of indices $k_1,\dots,k_m$ contains an even number.

UDC: 517.54

Received: 13.12.1995

DOI: 10.4213/mzm1554


 English version:
Mathematical Notes, 1997, 61:5, 609–613

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