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The Sharp Bound of Certain Second Hankel Determinants for the Class of Inverse of Starlike Functions with Respect to Symmetric Points

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Ukrainian Mathematical Journal Aims and scope

We investigate the sharp bound of certain coefficient functionals associated with a Hankel determinant of the second kind for the inverse function when f belongs to the class of starlike functions with respect to symmetric points.

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References

  1. R. M. Ali, “Coefficient of the inverse of strongly starlike functions,” Bull. Malays. Math. Sci. Soc., 26, 63–71 (2003).

    MathSciNet  Google Scholar 

  2. P. L. Duren, “Univalent functions,” Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer-Verlag, New York (1983).

    Google Scholar 

  3. T. Hayami and S. Owa, “Generalized Hankel determinant for certain classes,” Int. J. Math. Anal., 4(52), 2573–2585 (2010).

    MathSciNet  Google Scholar 

  4. A. L. P. Hern, A. Janteng, and R. Omar, “Hankel determinant H2(3) for certain subclasses of univalent functions,” Math. Stat., 8, No. 5, 566–569 (2020); DOI: https://doi.org/10.13189/ms.2020.080510.

    Article  Google Scholar 

  5. A. Janteng, S. A. Halim, and M. Darus, “Hankel determinant for starlike and convex functions,” Int. J. Math. Anal., 1, No. 13, 619–625 (2007).

    MathSciNet  Google Scholar 

  6. A. Janteng, S. A. Halim, and M. Darus, “Coefficient inequality for a function whose derivative has a positive real part,” J. Inequal. Pure Appl. Math., 7, No. 2, 1–5 (2006).

    MathSciNet  Google Scholar 

  7. O. S. Kwon, A. Lecko, and Y. J. Sim, “On the fourth coefficient of functions in the Carath´eodory class,” Comput. Methods Funct. Theory, 18, 307–314 (2018).

    Article  MathSciNet  Google Scholar 

  8. R. J. Libera and E. J. Zlotkiewicz, “Early coefficients of the inverse of a regular convex function,” Proc. Amer. Math. Soc., 85, No. 2, 225–230 (1982).

    Article  MathSciNet  Google Scholar 

  9. R. J. Libera and E. J. Zlotkiewicz, “Coefficient bounds for the inverse of a function with derivative in 𝒫,” Proc. Amer. Math. Soc., 87, No. 2, 251–257 (1983).

    MathSciNet  Google Scholar 

  10. Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen (1975).

    Google Scholar 

  11. T. Ramreddy and D. Vamshee Krishna, “Hankel determinant for starlike and convex functions with respect to symmetric points,” J. Indian Math. Soc. (N.S.), 79, No. 1–4, 161–171 (2012).

  12. B. Rath, K. S. Kumar, D. V. Krishna, and G. K. S. Viswanadh, “The sharp bound of the third Hankel determinants for inverse of starlike functions with respect to symmetric points,” Mat. Stud., 58, 45–50 (2022).

    Article  MathSciNet  Google Scholar 

  13. B. Rath, K. S. Kumar, D. V. Krishna, and A. Lecko, “The sharp bound of the third Hankel determinant for starlike functions of order 1/2,” Complex Anal. Oper. Theory, 16, No. 5, Paper No. 65 (2022); https://doi.org/10.1007/s11785-022-01241-8.

  14. K. Sakaguchi, “On a certain univalent mapping,” J. Math. Soc. Japan, 11, 72–75 (1959).

    Article  MathSciNet  Google Scholar 

  15. Y. J. Sim, A. Lecko, and D. K. Thomas, “The second Hankel determinant for strongly convex and Ozaki close-to-convex functions,” Ann. Mat. Pura Appl., 2515–2533 (2021); https://doi.org/10.1007/s10231-021-01089-3.

  16. P. Zaprawa, “On hankel determinant H2(3) for univalent functions,” Results Math., 73, No. 3, Paper No. 89 (2018); DOI.org/https://doi.org/10.1007/s00025-018-0854-1.

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Correspondence to Biswajit Rath.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 10, pp. 1377–1386, October, 2023. Ukrainian DOI: 10.37863/umzh.v75i10.7255.

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Kumar, K.S., Rath, B., Vani, N. et al. The Sharp Bound of Certain Second Hankel Determinants for the Class of Inverse of Starlike Functions with Respect to Symmetric Points. Ukr Math J 75, 1561–1572 (2024). https://doi.org/10.1007/s11253-024-02278-y

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  • DOI: https://doi.org/10.1007/s11253-024-02278-y

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