Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions

Varesha Sharma; Praveen Kumar Chaurasia

doi:10.63673/SJS.1882993

Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions

Abstract

In this paper, we determine the Second Hankel and Vandermonde determinants of the logarithmic inverse coefficients for the class $R_{tanh}$, a class of functions characterized by bounded boundary rotation and defined by a subordination condition involving the hyperbolic tangent function. The Vandermonde determinant has applications in diverse fields such as error-correcting codes, the Discrete Fourier Transform, representation theory, and the quantum Hall effect.

Keywords

References

Allu, V. and Arora, V. (2024). Second Hankel determinant of logarithmic coefficients of certain analytic functions. Rocky Mountain Journal of Mathematics, 54(2):343–359.
Andreev, V. V. and Duren, P. L. (1988). Inequalities for logarithmic coefficients of univalent functions and their derivatives. Indiana University Mathematics Journal, 37(4):721–733.
Arif, M., Raza, M., Ullah, I., and Zaprawa, P. (2022). Hankel determinants of order four for a set of functions with bounded turning of order α. Lithuanian Mathematical Journal, 62(2):135–145.
Bulut, S. (2024). Sharp bounds for the second Hankel determinant of logarithmic coefficients for parabolic starlike and uniformly convex functions of order alpha. Khayyam Journal of Mathematics, 10(1):51–69.
Choi, J. H., Kim, Y. C., and Sugawa, T. (2007). A general approach to the Fejér–Szegö problem. Journal of the Mathematical Society of Japan, 59(3):707–727.
Cik Soh, S., Mohamad, D., and Dzubaidi, H. (2024). Coefficient estimate of the second Hankel determinant of logarithmic coefficients for the subclass of close-to-convex functions. TWMS Journal of Applied and Engineering Mathematics, 24(2):563–570.
De Branges, L. (1985). A proof of the Bieberbach conjecture. Acta Mathematica, 154(1):137152.
Duren, P. L. (1983). Univalent Functions, volume 259. Springer Science & Business Media.

Efraimidis, I. (2016). A generalization of Livingston’s coefficient inequalities for functions with positive real part. Journal of Mathematical Analysis and Applications, 435(1):369–379.
Elhosh, M. M. (1996). On the logarithmic coefficients of close-to-convex functions. Journal of the Australian Mathematical Society, 60(1):1–6.
Kayumov, I. P. (2005). On Brennan’s conjecture for a special class of functions. Mathematical Notes, 78(3):498–502.
Khan, M. G., Mashwani, W. K., Ro, J. S., and Ahmad, B. (2023). Problems concerning sharp coefficient functionals of bounded turning functions. AIMS Mathematics, 8(11):27396–27413.
Li, Y. and Ding, X. (2023). Vandermonde determinant and its applications. Journal of Education and Culture Studies, 7(4):16–24.
Libera, R. J. and Zlotkiewicz, E. J. (1982). Early coefficient of the inverse of a regular convex function. Proceedings of the American Mathematical Society, 85(2):225–230.
Löwner, K. (1923). Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. i. Mathematische Annalen, 89(1):103–121.
Milin, I. M. (1977). Univalent functions and orthonormal systems, volume 49 of Translations of Mathematical Monographs. American Mathematical Society.
Mohamad, D., Wahid, N. H. A. A., and Hasni, N. N. (2023). Coefficient problems for starlike functions with respect to symmetric conjugate points connected to the sine function. European Journal of Pure and Applied Mathematics, 16(2):1167–1179.
Pommerenke, C. (1966). On the coefficients and Hankel determinants of univalent functions. Journal of the London Mathematical Society, 1(1):111–122.
Pommerenke, C. (1967). On the Hankel determinants of univalent functions. Mathematika, 14(1):108–112.
Ponnusamy, S., Sharma, N. L., and Wirths, K. J. (2018). Logarithmic coefficients of the inverse of univalent functions. Results in Mathematics, 73(4):160.
Ramírez, W. and Cesarano, C. (2022). Some new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler, and Apostol-genocchi polynomials. Carpathian Mathematical Publications, 14(2):354–363.
Ramírez, W., Cesarano, C., and Díaz, S. (2022). New results for degenerated generalized Apostol–Bernoulli, Apostol–Euler, and Apostol–Genocchi polynomials. WSEAS Transactions on Mathematics, 21:604–608.
Ullah, K., Zainab, S., Arif, M., Darus, M., and Shutaywi, M. (2021). Radius problems for starlike functions associated with the tan hyperbolic function. Journal of Function Spaces, 2021:9967640.
Vijayalakshmi, S. P., Bulut, S., and Sudharsan, T. V. (2022). Vandermonde determinant for a certain Sakaguchi-type function in the limacon domain. Asian-European Journal of Mathematics, 15(12):2250212.
Wahid, N. H. A. A., Tumiran, S., and Shaba, T. G. (2024). Hankel and Toeplitz determinants of logarithmic coefficients of inverse functions for the subclass of starlike functions with respect to symmetric conjugate points. European Journal of Pure and Applied Mathematics, 17(3):1818–1830.

Details

Primary Language

English

Subjects

Complex Systems in Mathematics

Journal Section

Research Article

Authors

Varesha Sharma ^*
0009-0002-7539-4107
India

Praveen Kumar Chaurasia
0009-0009-2580-6311
India

Publication Date

May 12, 2026

Submission Date

February 5, 2026

Acceptance Date

February 22, 2026

Published in Issue

Year 2026 Volume: 52 Number: 1

DOI

https://doi.org/10.63673/SJS.1882993

IZ

https://izlik.org/JA65YL77SG

Cite

RIS / Bibtex

APA

Sharma, V., & Chaurasia, P. K. (2026). Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions. Selcuk Journal of Science, 52(1), 60-73. https://doi.org/10.63673/SJS.1882993

AMA

1.Sharma V, Chaurasia PK. Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions. Selcuk J. Sci. 2026;52(1):60-73. doi:10.63673/SJS.1882993

Chicago

Sharma, Varesha, and Praveen Kumar Chaurasia. 2026. “Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions”. Selcuk Journal of Science 52 (1): 60-73. https://doi.org/10.63673/SJS.1882993.

EndNote

Sharma V, Chaurasia PK (May 1, 2026) Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions. Selcuk Journal of Science 52 1 60–73.

IEEE

[1]V. Sharma and P. K. Chaurasia, “Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions”, Selcuk J. Sci., vol. 52, no. 1, pp. 60–73, May 2026, doi: 10.63673/SJS.1882993.

ISNAD

Sharma, Varesha - Chaurasia, Praveen Kumar. “Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions”. Selcuk Journal of Science 52/1 (May 1, 2026): 60-73. https://doi.org/10.63673/SJS.1882993.

JAMA

1.Sharma V, Chaurasia PK. Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions. Selcuk J. Sci. 2026;52:60–73.

MLA

Sharma, Varesha, and Praveen Kumar Chaurasia. “Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions”. Selcuk Journal of Science, vol. 52, no. 1, May 2026, pp. 60-73, doi:10.63673/SJS.1882993.

Vancouver

1.Varesha Sharma, Praveen Kumar Chaurasia. Bounds for Determinants of Logarithmic Coefficients of Inverse Bounded Turning Functions. Selcuk J. Sci. 2026 May 1;52(1):60-73. doi:10.63673/SJS.1882993