Notes on Convex Functions of Order α

被引：0

作者：

Sugawa, Toshiyuki ^{[1
]}

Wang, Li-Mei ^{[2
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Aoba Ku, Sendai, Miyagi 9808579, Japan

[2] Univ Int Business & Econ, Sch Stat, 10 Huixin Dongjie, Beijing 100029, Peoples R China

来源：

COMPUTATIONAL METHODS AND FUNCTION THEORY | 2016年 / 16卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Subordination; Convex functions of order alpha; Hypergeometric function; UNIVALENT-FUNCTIONS; STARLIKE;

D O I：

10.1007/s40315-015-0122-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Marx and Strohhacker showed in 1933 that f(z) / z is subordinate to for a normalized convex function f on the unit disk In 1973, Brickman, Hallenbeck, MacGregor and Wilken further proved that f(z) / z is subordinate to if f is convex of order for and conjectured that this is true also for Here, is the standard extremal function in the class of normalized convex functions of order and We prove the conjecture and study geometric properties of convex functions of order In particular, we prove that is starlike whenever both f and g are convex of order 3 / 5.

引用

页码：79 / 92

页数：14

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