Sufficient Conditions for Janowski Starlikeness

Rosihan M. Ali, V. Ravichandran and N. Seenivasagan

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-7

Abstract:

Let A , B , D , E ∈ [ − 1 , 1 ] and let p ( z ) be an analytic function defined on the open unit disk, p ( 0 ) = 1 . Conditions on A , B , D , and E are determined so that 1 + β z p ' ( z ) being subordinated to ( 1 + D z ) / ( 1 + E z ) implies that p ( z ) is subordinated to ( 1 + A z ) / ( 1 + B z ) . Similar results are obtained by considering the expressions 1 + β ( z p ' ( z ) / p ( z ) ) and 1 + β ( z p ' ( z ) / p 2 ( z ) ) . These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:062925

DOI: 10.1155/2007/62925

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