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
R. M. Ali, “Coefficient of the inverse of strongly starlike functions,” Bull. Malays. Math. Sci. Soc., 26, 63–71 (2003).
P. L. Duren, “Univalent functions,” Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer-Verlag, New York (1983).
T. Hayami and S. Owa, “Generalized Hankel determinant for certain classes,” Int. J. Math. Anal., 4(52), 2573–2585 (2010).
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.
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).
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).
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).
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).
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).
Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen (1975).
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).
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).
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.
K. Sakaguchi, “On a certain univalent mapping,” J. Math. Soc. Japan, 11, 72–75 (1959).
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.
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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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