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Sufficient Conditions for Janowski Starlikeness

Author

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  • Rosihan M. Ali
  • V. Ravichandran
  • N. Seenivasagan

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.

Suggested Citation

  • Rosihan M. Ali & V. Ravichandran & N. Seenivasagan, 2007. "Sufficient Conditions for Janowski Starlikeness," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-7, August.
    • Handle: RePEc:hin:jijmms:062925
    DOI: 10.1155/2007/62925
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    Cited by:

    1. Najla M. Alarifi & Saiful R. Mondal, 2022. "On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    2. Saiful R. Mondal & Mohammed Al Dhuain, 2016. "Inclusion of the Generalized Bessel Functions in the Janowski Class," International Journal of Analysis, Hindawi, vol. 2016, pages 1-8, October.

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