DIFFERENTIAL SUBORDINATION FOR FUNCTIONS ASSOCIATED WITH THE LEMNISCATE OF BERNOULLI

被引：73
|
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
收藏
页码：1017 / 1026
页数：10
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