Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions
Abstract
:1. Introduction and Definitions
2. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- De Branges, L. A proof of the Bieberbach conjecture. Acta Math. 1985, 154, 137–152. [Google Scholar] [CrossRef]
- Ali, M.F.; Thomas, D.K.; Vasudevarao, A. Toeplitz determinants whose elements are the coefficients of analytic and univalent functions. Bull. Aust. Math. Soc. 2018, 97, 253–264. [Google Scholar] [CrossRef]
- Cantor, D.G. Power series with integral coefficients. Bull. Amer. Math. Soc. 1963, 69, 362–366. [Google Scholar] [CrossRef]
- Cudna, K.; Kwon, O.S.; Lecko, A.; Sim, Y.J.; Smiarowska, B. The second and third-order Hermitian Toeplitz determinants for starlike and convex functions of order alpha. Bol. Soc. Mat. Mex. 2020, 3, 361–375. [Google Scholar] [CrossRef]
- Allu, V.; Lecko, A.; Thomas, D.K. Hankel, Toeplitz, and Hermitian-Toeplitz determinants for certain close-to-convex functions. Mediterr. J. Math. 2022, 19, 22. [Google Scholar] [CrossRef]
- Cho, N.E.; Kumar, S.; Kumar, V. Hermitian-Toeplitz and Hankel determinants for certain starlike functions. Asian-Eur. J. Math. 2022, 15, 2250042. [Google Scholar] [CrossRef]
- Jastrzebski, P.; Kowalczyk, B.; Kwon, O.S.; Lecko, A.; Sim, Y.J. Hermitian Toeplitz determinants of the second and third-order for classes of close-to-star functions. Rev. Real Acad. Cienc. Exactas Físicas Nat. Ser. Matemtáicas 2020, 114, 166. [Google Scholar] [CrossRef]
- Kumar, V. Hermitian-Toeplitz determinants for certain classes of close-to-convex functions. Bull. Iran. Math. Soc. 2022, 48, 1093–1109. [Google Scholar] [CrossRef]
- Kowalczyk, B.; Kwon, O.S.; Lecko, A.; Sim, Y.J.; Smiarowska, B. The third-order Hermitian Toeplitz determinant for classes of functions convex in one direction. Bull. Malays. Math. Sci. Soc. 2020, 43, 3143–3158. [Google Scholar] [CrossRef]
- Kowalczyk, B.; Lecko, A.; Smiarowska, B. Sharp inequalities for Hermitian Toeplitz determinants for strongly starlike and strongly convex functions. J. Math. Inequal. 2021, 15, 323–332. [Google Scholar] [CrossRef]
- Lecko, A.; Smiarowska, B. Sharp bounds of the Hermitian Toeplitz determinants for some classes of close-to-convex functions. Bull. Malays. Math. Sci. Soc. 2021, 44, 3391–3412. [Google Scholar] [CrossRef]
- Obradovi, C.M.; Tuneski, N. Hermitian Toeplitz determinants for the class S of univalent functions. Armen. J. Math. 2021, 13, 649–654. [Google Scholar] [CrossRef]
- Kumar, V.; Kumar, S. Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions. Bol. Soc. Mat. Mex. 2021, 27, 55. [Google Scholar] [CrossRef]
- Lecko, A.; Sim, Y.J.; Smiarowska, B. The fourth-order Hermitian Toeplitz determinant for convex functions. Anal. Math. Phys. 2020, 10, 39. [Google Scholar] [CrossRef]
- Libera, R.J.; Złotkiewicz, E.J. Early coefficients of the inverse of a regular convex function. Proc. Amer. Math. Soc. 1982, 85, 225–230. [Google Scholar] [CrossRef]
- Libera, R.J.; Złotkiewicz, E.J. Coefficient bounds for the inverse of a function with derivatives in P. Proc. Amer. Math. Soc. 1983, 87, 251–257. [Google Scholar] [CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Ullah, W.; Fayyaz, R.; Breaz, D.; Cotîrlă, L.-I. Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions. Symmetry 2025, 17, 407. https://doi.org/10.3390/sym17030407
Ullah W, Fayyaz R, Breaz D, Cotîrlă L-I. Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions. Symmetry. 2025; 17(3):407. https://doi.org/10.3390/sym17030407
Chicago/Turabian StyleUllah, Wahid, Rabia Fayyaz, Daniel Breaz, and Luminiţa-Ioana Cotîrlă. 2025. "Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions" Symmetry 17, no. 3: 407. https://doi.org/10.3390/sym17030407
APA StyleUllah, W., Fayyaz, R., Breaz, D., & Cotîrlă, L.-I. (2025). Sharp Bounds of Hermitian Toeplitz Determinants for Bounded Turning Functions. Symmetry, 17(3), 407. https://doi.org/10.3390/sym17030407