A bound for the coefficient c4 for one-sheeted functions in terms of ¦c2¦期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A bound for the coefficient c4 for one-sheeted functions in terms of ¦c2¦

Authors:	V. A. Baranova

Affiliation:	(1) Leningrad State University, USSR

Abstract:	In the class S of functions $f(z) = z + sumnolimits_{k = 2}^infty {c_k z^k }$ which are regular and single-sheeted in the circle ¦z¦ < 1, the bound for ¦c₄¦ in terms of ¦c₂¦, obtained by Al'fors, is improved. The crudest bound ¦c₄¦ –< 4/15 (11 + ¦c₂¦) is better than that of Al'fors: ¦c₄¦ –< $left\| {c_4 } right\| leqslant ({4 mathord{left/ {vphantom {4 {sqrt {15} }}} right. kern-nulldelimiterspace} {sqrt {15} }})sqrt {11 + left\| {1c_2 } right\|^2 } .$ Translated from Matematicheskie Zametki, Vol. 12, No. 2, pp. 127–130, August, 1972.

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