We establish an upper bound for the Hankel determinants of certain orders linked with the kth-root transform \({\left[f\left({z}^{k}\right)\right]}^\frac{1}{k}\) of the holomorphic mapping f(z) whose derivative has a positive real part with normalization, namely, f(0) = 0 and f′(0) = 1.
Similar content being viewed by others
References
R. M. Ali, S. K. Lee, V. Ravichandran, and S. Supramaniam, “The Fekete–Szegö coefficient functional for transforms of analytic functions,” Bull. Iranian Math. Soc., 35, No. 2, 119–142 (2009).
A. K. Bakhtin and I. V. Denega, “Extremal decomposition of the complex plane with free poles,” J. Math. Sci. (N.Y.), 246, No. 1, 1–17 (2020).
I. Denega, “Extremal decomposition of the complex plane for n-radial system of points,” Azerb. J. Math., Special Issue Dedicated to the 67th Birth Anniversary of Prof. M. Mursaleen, 64–74 (2021).
P. L. Duren, “Univalent functions,” Grundlehren Math. Wiss., 259, Springer, New York (1983).
T. Hayami and S. Owa, “Generalized Hankel determinant for certain classes,” Int. J. Math. Anal., 4, No. 52, 2573–2585 (2010).
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).
A. E. Livingston, “The coefficients of multivalent close-to-convex functions,” Proc. Amer. Math. Soc., 21, No. 3, 545–552 (1969).
T. H. MacGregor, “Functions whose derivative have a positive real part,” Trans. Amer. Math. Soc., 104, No. 3, 532–537 (1962).
Ch. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen (1975).
Ch. Pommerenke, “On the coefficients and Hankel determinants of univalent functions,” J. London Math. Soc., 41, 111–122 (1966).
P. Zaprawa, “On Hankel determinant H2(3) for univalent functions,” Res. Math., 73, No. 3, Article 89 (2018).
P. Zaprawa, “Third Hankel determinants for subclasses of univalent functions,” Mediterran. J. Math., 14, No. 1, 1–10 (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 12, pp. 1673–1678, December, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i12.6671.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Vani, N., Vamshee Krishna, D. & Shalini, D. Some Coefficient Bounds Associated with Transforms of Bounded Turning Functions. Ukr Math J 74, 1909–1915 (2023). https://doi.org/10.1007/s11253-023-02177-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-023-02177-8