DIFFERENTIAL SUBORDINATION FOR FUNCTIONS ASSOCIATED WITH THE LEMNISCATE OF BERNOULLI

Conditions onβare determined so that 1 +βzp′(z) subordinated to 1 + z impliespis subordinated to 1 + z . Analogous results are also obtained involving the expressions 1 +βzp′(z)/p(z) and 1 +βzp′(z)/p 2(z). These results are applied to obtain sufficient conditions for normalized analytic functionsfto...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 16; no. 3; pp. 1017 - 1026
Main Authors Ali, Rosihan M., Cho, Nak Eun, Ravichandran, V., Kumar, S. Sivaprasad
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2012
Subjects
Analytic functions
Differentials
Mathematical functions
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Summary:Conditions onβare determined so that 1 +βzp′(z) subordinated to 1 + z impliespis subordinated to 1 + z . Analogous results are also obtained involving the expressions 1 +βzp′(z)/p(z) and 1 +βzp′(z)/p 2(z). These results are applied to obtain sufficient conditions for normalized analytic functionsfto satisfy the condition |(zf′(z)/f(z))2− 1| < 1. 2010Mathematics Subject Classification: Primary 30C45; Secondary 30C80. Key words and phrases: Starlike functions, Lemniscate of Bernoulli, Differential subordination, Differential superordination, Best subordinant, Best dominant.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406676