Hostname: page-component-55f67697df-zh294 Total loading time: 0 Render date: 2025-05-10T04:11:42.375Z Has data issue: false hasContentIssue false
  • English
  • Français

THE THIRD HANKEL DETERMINANT FOR INVERSE COEFFICIENTS OF CONVEX FUNCTIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  02 May 2023

MOHSAN RAZA Open the ORCID record for MOHSAN RAZA [Opens in a new window] ,
AMINA RIAZ Open the ORCID record for AMINA RIAZ [Opens in a new window]  and
DEREK K. THOMAS Open the ORCID record for DEREK K. THOMAS [Opens in a new window]
MOHSAN RAZA*
Affiliation:
Department of Mathematics, Government College University, Faisalabad, Pakistan
AMINA RIAZ
Affiliation:
Department of Mathematics, COMSATS University Isalamabad, Lahore Campus, Pakistan e-mail: [email protected]
DEREK K. THOMAS
Affiliation:
School of Mathematics and Computer Science, Swansea University, Bay Campus, Swansea SA1 8EN, UK e-mail: [email protected]
*
e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The sharp bound for the third Hankel determinant for the coefficients of the inverse function of convex functions is obtained, thus answering a recent conjecture concerning invariance of coefficient functionals for convex functions.

Keywords

univalentstarlikeconvex functionHankel determinantinverse coefficientsinvariance

MSC classification

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C50: Coefficient problems for univalent and multivalent functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 109 , Issue 1 , February 2024 , pp. 94 - 100
Check for updates
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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

Banga, S. and Kumar, S. S., ‘The sharp bounds of the second and third Hankel determinants for the class ${\mathbf{\mathcal{SL}}}^{\ast }$ ’, Math. Slovaca 70 (2020), 849–862.CrossRefGoogle Scholar
Cho, N. E., Kowalczyk, B., Kwon, O. S., Lecko, A. and Sim, Y. J., ‘The bounds of some determinants for starlike functions of order alpha’, Bull. Malays. Math. Sci. Soc. 41 (2018), 523–535.CrossRefGoogle Scholar
Janteng, A., Halim, S. A. and Darus, M., ‘Coeffcient inequality for a function whose derivative has a positive real part’, J. Inequal. Pure Appl. Math. 7(2) (2006), 1–5.Google Scholar
Kowalczyk, B., Lecko, A., Lecko, M. and Sim, Y. J., ‘The sharp bound of the third Hankel determinant for some classes of analytic functions’, Bull. Korean Math. Soc. 55 (2018), 1859–1868.Google Scholar
Kowalczyk, B., Lecko, A. and Sim, Y. J., ‘The sharp bound of the Hankel determinant of the third kind for convex functions’, Bull. Aust. Math. Soc. 97 (2018), 435–445.CrossRefGoogle Scholar
Kwon, O. S., Lecko, A. and Sim, Y. J., ‘On the fourth coefficient of functions in the Carathéodory class’, Comput. Methods Funct. Theory 18 (2018), 307–314.CrossRefGoogle Scholar
Kwon, O. S., Lecko, A. and Sim, Y. J., ‘The bound of the Hankel determinant of the third kind for starlike functions’, Bull. Malays. Math. Sci. Soc. 42 (2019), 767–780.CrossRefGoogle Scholar
Lecko, A., Sim, Y. J. and Smiarowska, B., ‘The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2’, Complex Anal. Oper. Theory 13 (2019), 2231–2238.CrossRefGoogle Scholar
Lee, S. K., Ravichandran, V. and Supramanian, S., ‘Bound for the second Hankel determinant of certain univalent functions’, J. Inequal. Appl. 2013(281) (2013), 1–17.CrossRefGoogle Scholar
Libera, R. J. and Zlotkiewicz, E. J., ‘Early coefficients of the inverse of a regular convex functions’, Proc. Amer. Math. Soc. 85 (1982), 225–230.CrossRefGoogle Scholar
Pommerenke, C., ‘On the coefficients and Hankel determinants of univalent functions’, J. Lond. Math. Soc. (2) 14 (1966), 111–122.CrossRefGoogle Scholar
Raducanu, D. and Zaprawa, P., ‘Second Hankel determinant for the close-to-convex functions’, C. R. Math. Acad. Sci. Paris 355(10) (2017), 1063–1071.CrossRefGoogle Scholar
Riaz, A., Raza, M. and Thomas, D. K., ‘Hankel determinants for starlike and convex functions associated with sigmoid functions’, Forum Math. 34 (2022), 137–156.CrossRefGoogle Scholar
Sim, Y. J., Lecko, A. and Thomas, D. K., ‘The second Hankel determinant for strongly convex and Ozaki close-to-convex functions’, Ann. Mat. Pura Appl. (4) 200 (2021), 2515–2533.CrossRefGoogle Scholar
Sokól, J. and Thomas, D. K., ‘The second Hankel determinant for alpha-convex functions’, Lith. Math. J. 58 (2018), 212–218.CrossRefGoogle Scholar
Thomas, D. K., ‘Coefficient invariances for convex functions’, Congressio Mathematica VIII, to appear, arXiv:2212.04929.Google Scholar