DIFFERENTIAL SUBORDINATION FOR FUNCTIONS ASSOCIATED WITH THE LEMNISCATE OF BERNOULLI

被引：75

作者：

Ali, Rosihan M. ^{[2
]}

Cho, Nak Eun ^{[1
]}

Ravichandran, V. ^{[3
]}

Kumar, S. Sivaprasad ^{[4
]}

机构：

[1] Pukyong Natl Univ, Dept Appl Math, Pusan 608737, South Korea

[2] Univ Sains Malaysia, Sch Math Sci, George Town 11800, Malaysia

[3] Univ Delhi, Dept Math, Delhi 110007, India

[4] Delhi Technol Univ, Dept Appl Math, Delhi 110042, India

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2012年 / 16卷 / 03期

基金：

新加坡国家研究基金会;

关键词：

Starlike functions; Lemniscate of Bernoulli; Differential subordination; Differential superordination; Best subordinant; Best dominant; STARLIKENESS;

D O I：

10.11650/twjm/1500406676

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Conditions on beta are determined so that 1 + beta zp' (z) subordinated to root 1 + z implies p is subordinated to root 1 + z. Analogous results are also obtained involving the expressions 1+ beta zp' (z)/p(z) and 1+ beta zp'(z)/p(2)(z). These results are applied to obtain sufficient conditions for normalized analytic functions f to satisfy the condition vertical bar(zf'(z)/f(z))(2) - 1 vertical bar < 1.

引用

页码：1017 / 1026

页数：10

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