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Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses

Author

Listed:
  • Aaisha Farzana Habibullah

    (Department of Mathematics with Computer Applications, A. M. Jain College, Meenambakkam, Chennai 600061, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Muthusamy Palani Jeyaraman

    (Department of Mathematics, L. N. Government College, Ponneri, Chennai 601204, Tamil Nadu, India
    These authors contributed equally to this work.)

  • Teodor Bulboacă

    (Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

Abstract

For a function p analytic in the open unit disc and satisfying p ( 0 ) = 1 , we prove certain subordination implications of the first order differential subordination 1 + z p ′ ( z ) ≺ 1 + M z , which provides sufficient conditions for a function to belong to various subclasses of Ma-Minda starlike functions. The pre-Schwarzian norm estimate and inclusion criteria for certain subclasses of analytic function are also obtained. Additionally, using Gronwall’s inequality we give a sufficient condition for a normalized function to belong to a class of functions with bounded arguments that extends the class of strongly α -Bazilevič functions of order γ studied by Gao in 1996.

Suggested Citation

  • Aaisha Farzana Habibullah & Muthusamy Palani Jeyaraman & Teodor Bulboacă, 2022. "Subordinations and Norm Estimates for Functions Associated with Ma-Minda Subclasses," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2879-:d:886049
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    References listed on IDEAS

    as
    1. T. N. Shanmugam, 1989. "Convolution and differential subordination," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-8, January.
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