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On Lemniscate Starlikeness of the Solution of General Differential Equations

Author

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  • Saiful R. Mondal

    (Department of Mathematics and Statistics, Collage of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia)

Abstract

In this article, we derived conditions on the coefficient functions a ( z ) and b ( z ) of the differential equations y ″ ( z ) + a ( z ) y ′ ( z ) + b ( z ) y ( z ) = 0 and z 2 y ″ ( z ) + a ( z ) z y ′ ( z ) + b ( z ) y ( z ) = 0 , such their solution f ( z ) with normalization f ( 0 ) = 0 = f ′ ( 0 ) − 1 is starlike in the lemniscate domain, equivalently z f ′ ( z ) / f ( z ) ≺ 1 + z . We provide several examples with graphical presentations for a clear view of the obtained results.

Suggested Citation

  • Saiful R. Mondal, 2022. "On Lemniscate Starlikeness of the Solution of General Differential Equations," Mathematics, MDPI, vol. 10(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3254-:d:909313
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    References listed on IDEAS

    as
    1. 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.
    2. Selinger, V., 1995. "Geometric properties of normalized Bessel functions," Pure Mathematics and Applications, Department of Mathematics, Corvinus University of Budapest, vol. 6(2-3), pages 273-277.
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