Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain

Bilal Şeker; Bilal Çekiç; Sevtap Sümer; Onur Akçiçek

doi:10.36753/mathenot.1592896

EN

Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain

Abstract

In this paper, we first obtained some initial logarithmic coefficient bounds on a subclass of bounded turning functions $\mathcal{R}_{\mathcal{L}}$ related to a lune domain. For functions belonging to this class, we determined the sharp bounds for the second Hankel determinant of logarithmic coefficients $H_{2,1}\left( F_{f}/2\right) $ of bounded turning functions related to a lune domain. Finally, we calculated the bounds of third Hankel determinant of logarithmic coefficients $H_{3,1}\left( F_{f}/2\right)$ of bounded turning functions associated with a lune domain.

Keywords

Bounded Turning Functions, Hankel determinant, Logarithmic coefficients

References

[1] Ma, W. C., Minda, D.: A unified treatment of some special classes of univalent functions. In: Proceedings of the Proceedings of the Conference on Complex Analysis. Tianjin, China, 157-169 (19–23 June 1992).
[2] Sharma, P., Raina, R. K., Sokół, J.: Certain Ma–Minda type classes of analytic functions associated with the crescent-shaped region. Analysis and Mathematical Physics. 9, 1–17 (2019).
[3] Wani, L. A., Swaminathan, A.: Starlike and convex functions associated with a Nephroid domain. Bulletin of the Malaysian Mathematical Sciences Society. 44, 79–104 (2021).
[4] Kumar, S. S., Kamaljeet, G.: A cardioid domain and starlike functions. Analysis and Mathematical Physics. 11, 54 (2021).
[5] Malik, S. N, Raza, M., Xin, Q., Sokol, J., Manzoor, R., Zainab, S. : On convex functions associated with symmetric cardioid domain. Symmetry. 13(12), 2321 (2021).
[6] Mandal S, Ahamed MB: Second Hankel determinant of logarithmic coefficients for starlike and convex functions associated with lune. arXiv preprint, arXiv:2307.02741.(2023).
[7] Duren, P. L., Leung, Y. J.: Logarithmic coefficients of univalent functions. Journal d’Analyse Mathématique. 36(1), 36-43(1979).
[8] Cho, N. E., Kowalczyk, B., Kwon, O.S., Lecko, A., Sim, Y.J.: On the third logarithmic coefficient in some subclasses of close-to-convex functions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 114(2), 1-14 (2020).
[9] Thomas, D. K.: On logarithmic coefficients of close to convex functions. Proceedings of the American Mathematical Society. 144, 1681-1687 (2016).
[10] Zaprawa, P.: Initial logarithmic coefficients for functions starlike with respect to symmetric points. Boletin De La Sociedad Matematica Mexicana. 27(3), 1-13 (2021).

[11] Fekete, M., Szegö, G.: Eine Bemerkung Über ungerade schlichte Funktionen. Journal of the London Mathematical Society. 8, 85–89 (1933).
[12] Cho, N. E., Kowalczyk, B., Kwon, O. S., Lecko, A., Sim, Y. J.: Some coefficient inequalities related to the Hankel determinant for strongly starlike functions of order alpha. Journal of Mathematical Inequalities. 11(2), 429-439 (2017).
[13] Deniz, E., Özkan, Y., Kazımoglu, S.: Logarithmic coefficients for starlike functions associated with generalized telephone numbers. Filomat. 38(20), 7041-7050 (2024).
[14] Deniz, E., Budak, L.: Second Hankel determinant for certain analytic functions satisfying subordinate condition. Mathematica Slovaca. 68(2), 463-471(2018).
[15] Janteng, A., Halim, S. A., Darus, M.: Hankel determinant for starlike and convex functions. International Journal of Mathematical Analysis. 1(1), 619-625 (2007).
[16] Kazımoglu, S., Deniz, E., Srivastava, H. M.: Sharp coefficients bounds for starlike functions associated with Gregory coefficients. Complex Analysis and Operator Theory. 18(1), 6 (2024).
[17] Kowalczyk, B., Lecko, A., Sim, Y. J.: The sharp bound for the Hankel determinant of the third kind for convex functions. Bulletin of the Australian Mathematical Society. 97, 435-445 (2018).
[18] Krishna, D. V., Ramreddy, T.: Hankel determinant for starlike and convex functions of order alpha. Tbilisi Mathematical Journal. 5(1), 65-76 (2012).
[19] Lee, S. K., Ravichandran, V., Supramaniam, S.: Bounds for the second Hankel determinant of certain univalent functions. Journal of Inequalities and Applications. 281, (2013).
[20] Shi, L., Srivastava, H. M., Arif, M., Hussain, S., Khan, H.: An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential function. Symmetry. 11, 1-14 (2019).
[21] Sim, Y.J., Lecko, A., Thomas, D. K.: The second Hankel determinant for strongly convex and Ozaki close-to-convex functions. Annals of Mathematics. 200, 2515-2533 (2021).
[22] Sokol, J., Thomas, D. K.: The second Hankel determinant for alpha-convex functions. Lithuanian Mathematical Journal. 58(2), 212-218 (2018).
[23] Srivastava, H. M., Ahmad, Q. Z., Darus, M., Khan, N., Khan, B., Zaman, N., Shah, H. H.: Upper bound of the third Hankel determinant for a subclass of close-to-convex functions associated with the lemniscate of Bernoulli. Mathematics. 7, 1-10 (2019).
[24] Girela, D.: Logarithmic coefficients of univalent functions. Annales Academiæ Scientiarum Fennicæ Mathematica. 25 (2), 337–350 (2000).
[25] Obradovic, M., Ponnusamy, S., Wirths, K. J.: Logarithmic coefficients and a coefficient conjecture for univalent functions. Monatshefte für Mathematik. 185, 489-501 (2018).
[26] Ponnusamy, S., Sharma, N. L., Wirths, K. J.: Logarithmic coefficients problems in families related to starlike and convex functions. The Journal of the Australian Mathematical Society. 109(2), 230-249, (2020).
[27] Kowalczyk, B., Lecko, A.: Second Hankel determinant of logarithmic coefficients of convex and starlike functions. Bulletin of the Australian Mathematical Society. 105(3), 458-467 (2022).
[28] Kowalczyk, B., Lecko, A.: Second Hankel determinant of logarithmic coefficients of convex and starlike functions of order alpha. Bulletin of the Malaysian Mathematical Sciences Society. 45, 727-740 (2022).
[29] Sümer Eker S., Şeker B., Çekiç B., Acu M.: Sharp bounds for the second Hankel determinant of logarithmic coefficients for strongly starlike and strongly convex functions. Axioms, 11(8), 369 (2022).
[30] Srivastava H. M., Sümer Eker S., Şeker B., Çekiç B.: Second Hankel determinant of logarithmic coefficients for a subclass of univalent functions. Miskolc Mathematical Notes. 25, 479-488 (2024).
[31] Sümer Eker S., Lecko A., Çekiç B., Şeker B.: The second Hankel determinant of logarithmic coefficients for strongly Ozaki close-to-convex functions. Bulletin of the Malaysian Mathematical Sciences Society. 46(6), 183, (2023).
[32] Shi, L., Arif, M., Iqbal, J., Ullah, K., Ghufran, S.M.: Sharp bounds of Hankel determinant on logarithmic coefficients for functions starlike with exponential function. Fractal and Fractional. 6 (11), 645 (2022).
[33] Cho, N., Kowalczyk, B., Lecko, A.: Sharp bounds of some coefficient functionals over the class of functions convex in the direction of the imaginary axis. Bulletin of the Australian Mathematical Society. 100(1), 86-96 (2019).
[34] Pommerenke, C.: Univalent Functions. Vanderhoeck, Ruprecht, Gottingen, Germany, (1975).
[35] Keogh, F. R., Merkes, E. P.: A coefficient inequality for certain classes of analytic functions. Proceedings of the American Mathematical Society. 20, 8–12 (1969).
[36] Arif, M., Raza, M., Tang, H., Hussain, S., Khan, H.: Hankel determinant of order three for familiar subsets of analytic functions related with sine function. Open Mathematics. 17, 1615–1630 (2019).
[37] Choi, J.H., Kim, Y.C., Sugawa, T.: A general approach to the Fekete-Szegö problem. The Journal of the Mathematical Society of Japan. 59, 707-727 (2007).

Details

Primary Language

English

Subjects

Applied Mathematics (Other)

Journal Section

Research Article

Authors

Bilal Şeker ^*
0000-0003-1777-8145
Türkiye

Bilal Çekiç
0000-0002-6408-0455
Türkiye

Sevtap Sümer
0000-0002-2573-0726
Türkiye

Onur Akçiçek
0009-0008-9721-5345
Türkiye

Early Pub Date

May 19, 2025

Publication Date

June 26, 2025

Submission Date

November 29, 2024

Acceptance Date

May 4, 2025

Published in Issue

Year 2025 Volume: 13 Number: 2

DOI

https://doi.org/10.36753/mathenot.1592896

IZ

https://izlik.org/JA35FC82MZ

APA

Şeker, B., Çekiç, B., Sümer, S., & Akçiçek, O. (2025). Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain. Mathematical Sciences and Applications E-Notes, 13(2), 72-83. https://doi.org/10.36753/mathenot.1592896

AMA

1.Şeker B, Çekiç B, Sümer S, Akçiçek O. Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain. Math. Sci. Appl. E-Notes. 2025;13(2):72-83. doi:10.36753/mathenot.1592896

Chicago

Şeker, Bilal, Bilal Çekiç, Sevtap Sümer, and Onur Akçiçek. 2025. “Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated With Lune Domain”. Mathematical Sciences and Applications E-Notes 13 (2): 72-83. https://doi.org/10.36753/mathenot.1592896.

EndNote

Şeker B, Çekiç B, Sümer S, Akçiçek O (June 1, 2025) Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain. Mathematical Sciences and Applications E-Notes 13 2 72–83.

IEEE

[1]B. Şeker, B. Çekiç, S. Sümer, and O. Akçiçek, “Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain”, Math. Sci. Appl. E-Notes, vol. 13, no. 2, pp. 72–83, June 2025, doi: 10.36753/mathenot.1592896.

ISNAD

Şeker, Bilal - Çekiç, Bilal - Sümer, Sevtap - Akçiçek, Onur. “Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated With Lune Domain”. Mathematical Sciences and Applications E-Notes 13/2 (June 1, 2025): 72-83. https://doi.org/10.36753/mathenot.1592896.

JAMA

1.Şeker B, Çekiç B, Sümer S, Akçiçek O. Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain. Math. Sci. Appl. E-Notes. 2025;13:72–83.

MLA

Şeker, Bilal, et al. “Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated With Lune Domain”. Mathematical Sciences and Applications E-Notes, vol. 13, no. 2, June 2025, pp. 72-83, doi:10.36753/mathenot.1592896.

Vancouver

1.Bilal Şeker, Bilal Çekiç, Sevtap Sümer, Onur Akçiçek. Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Lune Domain. Math. Sci. Appl. E-Notes. 2025 Jun. 1;13(2):72-83. doi:10.36753/mathenot.1592896

Cited By

New Results on Analytic Function Subclasses Defined by Tangent Hyperbolic Functions

Axioms

https://doi.org/10.3390/axioms15030173

INDEXING & ABSTRACTING & ARCHIVING

20477 The published articles in MSAEN are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.