Hostname: page-component-55f67697df-zh294 Total loading time: 0 Render date: 2025-05-12T12:23:00.431Z Has data issue: false hasContentIssue false
  • English
  • Français

Second Hankel determinant of logarithmic coefficients of inverse strongly starlike functions

Part of: Geometric function theory

Published online by Cambridge University Press:  08 November 2024

Adam Lecko Open the ORCID record for Adam Lecko [Opens in a new window]  and
Barbara Śmiarowska Open the ORCID record for Barbara Śmiarowska [Opens in a new window]
Adam Lecko*
Affiliation:
Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland
Barbara Śmiarowska
Affiliation:
Department of Complex Analysis, Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland
*
Corresponding author: Adam Lecko, email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The sharp bound of the second Hankel determinant of logarithmic coefficients of inverse functions of strongly starlike functions is computed.

Keywords

univalent functionstarlike functionstrongly starlike functioninverse functionlogarithmic coefficientsHankel determinant

MSC classification

Primary: 30C50: Coefficient problems for univalent and multivalent functions
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 67 , Issue 4 , November 2024 , pp. 1196 - 1211
Check for updates
Copyright
© The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Brannan, D. A. and Kirwan, W. E., On some classes of bounded univalent functions, J. London Math. Soc. 2(1): (1969), 431–443.CrossRefGoogle Scholar
Cho, N. E., Kowalczyk, B., Kwon, O. S., Lecko, A. and Sim, Y. J., The bound of the Hankel determinant for strongly starlike functions of order alpha, J. Math. Inequal. 11(2), (2017), 429–439.CrossRefGoogle Scholar
Cho, N. E., Kowalczyk, B. and Lecko, A., Sharp bounds of some coefficient functionals over the class of functions convex in the direction of the imaginary axis, Bull. Aust. Math. Soc. 100(1), (2019), 86–96.CrossRefGoogle Scholar
Choi, J. H., Kim, Y. C. and Sugawa, T., A general approach to the Fekete–Szegö problem, J. Math. Soc. Japan. 59(3), (2007), 707–727.CrossRefGoogle Scholar
Duren, P. L., Univalent Functions (Springer-Verlag, 1983).Google Scholar
Goodman, A. W., Univalent Functions (Mariner Publishing Company, Inc., Tampa, Florida, 1983).Google Scholar
Jameson, G. J. O., Counting zeros of generalized polynomials: Descartes’ rule of signs and Laguerre’s extensions, Math. Gazette 90(518), (2006), 223–234.CrossRefGoogle Scholar
Kowalczyk, B. and Lecko, A., Second Hankel determinant of logarithmic coefficients of convex and starlike functions, Bull. Aust. Math. Soc. 105(3), (2022), 458–467.CrossRefGoogle Scholar
Kowalczyk, B. and Lecko, A., Second Hankel determinant of logarithmic coefficients of convex and starlike functions of order alpha, Bull. Malays. Math. Sci. Soc. 45(2), (2022), 727–740.CrossRefGoogle Scholar
Kowalczyk, B., Lecko, A. and Sim, Y. J., The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc. 97(3), (2018), 435–445.CrossRefGoogle Scholar
Kowalczyk, B., Lecko, A. and Thomas, D. K., The sharp bound of the third Hankel determinant for starlike functions, Forum Math. 34(5), (2022), 1249–1254.Google Scholar
Laguerre, E. N., Sur la théeorie des équations numériques, J. Math. Pures Appl. 9 (1883), 99–146. Oeuvres de Laguerre Vol. 1, Paris, 1898, 3–47.Google Scholar
Lecko, A., Some Methods in the Theory of Univalent Functions (Oficyna Wydawnicza Poltechniki Rzeszowskiej, Rzeszów, 2005).Google Scholar
Lecko, A., Strongly starlike and spirallike functions, Ann. Polon. Math. 85(2), (2005), 165–192.CrossRefGoogle Scholar
Ma, W. and Minda, D., An internal geometric characterization of strongly starlike functions, Ann. Univ. Mariae Curie Skłodowska Sect. A 45(11), (1991), 89–97.Google Scholar
Milin, I. M., Univalent Functions and Orthonormal Systems, Nauka, Moscow, 1971 (in Russian); English Translation, Translations of Mathematical Monographs, 49 (American Mathematical Society, Providence, RI, 1977).Google Scholar
Pommerenke, C., Univalent Functions (Vandenhoeck & Ruprecht, Göttingen, 1975).Google Scholar
Stankiewicz, J., Quelques problèmes extrémaux dans les classes des fonctions α-angulairement étoilées, Ann. Univ. Mariae Curie Skłodowska Sect. A 20(6), (1966), 59–75.Google Scholar
Stankiewicz, J., On a family of starlike functions, Ann. Univ. Mariae Curie Skłodowska Sect. A 22–24(27), (1968-1970), 175–181.Google Scholar
Sugawa, T., A self-duality of strong starlikeness, Kodai Math. J. 28(2), (2005), 382–389.CrossRefGoogle Scholar
Turowicz, A., Geometria zer wielomianów (Geometry of Zeros of Polynomials), Warszawa, PWN (1967) in Polish.Google Scholar