KaydedilenlerDerginizi ekleyin

Dergiler / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2026 / Volume: 14 Issue: 2

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

Onur Akçiçek(TOBB izzettin Dündar Anadolu Lisesi)0009-0008-9721-5345
Bilal Şeker(BATMAN ÜNİVERSİTESİ)0000-0003-1777-8145
Sayfa
—
Yayın Tarihi
2025-06-30
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In conclusion, we computed the bounds of the third Hankel determinant of logarithmic coefficients H_3,1 (F_f \/2).

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we initially established bounds for the logarithmic coefficients concerning a specific subclass of bounded turning functions R_℘ that are linked to the cardioid domain.
📊
Temel Bulgular & Veri:For the functions belonging to this class, we identified sharp bounds for the second Hankel determinant of logarithmic coefficients, denoted as H_2,1 (F_f \/2).
💡
Sonuç & Katkı:In conclusion, we computed the bounds of the third Hankel determinant of logarithmic coefficients H_3,1 (F_f \/2).
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Logarithmic coefficients · Hankel determinant · Bounded Turning Functions.

Abstract

In this study, we initially established bounds for the logarithmic coefficients concerning a specific subclass of bounded turning functions R_℘ that are linked to the cardioid domain. For the functions belonging to this class, we identified sharp bounds for the second Hankel determinant of logarithmic coefficients, denoted as H_2,1 (F_f \/2). In conclusion, we computed the bounds of the third Hankel determinant of logarithmic coefficients H_3,1 (F_f \/2).

🔖

Bu Makaleye Atıf Yap

Akçiçek, O., Şeker, B. (2025). Hankel Determinants of Logarithmic Coefficients for the Class of Bounded Turning Functions Associated with Cardioid Domain. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Volume: 14 Issue: 2. https://doi.org/10.17798/bitlisfen.1583030

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (33)

  1. M. Arif, M. Raza, H. Tang, S. Hussain and H. Khan, “Hankel determinant of order three for familiar subsets of analytic functions related with sine function,” Open Math., vol. 17, pp. 1615-1630. 2019.
  2. J. H. Choi, Y. C. Kim and T. Sugawa, “A general approach to the Fekete-Szegö problem,” J. Math. Soc. Japan, vol. 59, pp. 707-727. 2007.
  3. N. E. Cho, B. Kowalczyk, O. S. Kwon, A. Lecko and Y. J. Sim, “Some Coefficient Inequalities Related to the Hankel Determinant for Strongly Starlike Functions of Order Alpha,” J. Math. Inequal., vol. 11, pp. 429-439. 2017.
  4. N. E. Cho, B. Kowalczyk and A. Lecko, “Sharp Bounds of Some Coefficient Functionals Over The Class of Functions Convex in The Direction of the Imaginary Axis,” Bull. Aust. Math. Soc., vol. 100, pp. 86-96. 2019.
  5. N. E. Cho, B. Kowalczyk, O. S. Kwon, A. Lecko and Y. J. Sim, “On the third logarithmic coefficient in some subclasses of close-to-convex functions,” Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., vol. 114, pp. 1-14. 2020.
  6. D. Girela, “Logarithmic coefficients of univalent functions,” Ann. Acad. Sci. Fenn. Math., vol. 25, pp. 337-350. 2000.
  7. F.R. Keogh, E. P. Merkes, “A coefficient inequality for certain classes of analytic functions,” Proc. Am. Math. Soc., vol. 20, pp. 8-12. 1969.
  8. B. Kowalczyk, A. Lecko and Y. J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc., vol. 97, pp. 435-445. 2018.
  9. B. Kowalczyk, A. Lecko, “Second Hankel determinant of logarithmic coefficients of convex and starlike functions,” Bull. Aust. Math. Soc., vol. 105, pp. 458-467. 2022.
  10. B. Kowalczyk, A. Lecko, “Second Hankel determinant of logarithmic coefficients of convex and starlike functions of order alpha,” Bull. Malays. Math. Sci. Soc., vol. 45, pp. 727-740. 2022.
  11. W. C. Ma, D. Minda, “A unified treatment of some special classes of univalent functions,” in: Proceedings of the Proceedings of the Conference on Complex Analysis, Tianjin(China): International Press, 1992. pp. 157-169.
  12. S. Mandal, M.B. Ahamed, “Second Hankel determinant of Logarithmic coefficients for Starlike and Convex functions associated with lune,” arXiv.org, [Online]. Available: https://arxiv.org/pdf/2307.02741. [Accessed: Jul. 6, 2023].
  13. R. Mendiratta, S. Nagpal and V. Ravichandran, “On a subclass of strongly starlike functions associated exponential function,” Bull. Malays. Math. Sci. Soc., vol. 38, pp. 365-386. 2015.
  14. N. H. Mohammed, “Sharp bounds of logarithmic coefficient problems for functions with respect to symmetric points”, Mat. Stud., vol. 59, no. 1, pp. 68-75. 2023.
  15. M. Obradovi´c, S. Ponnusamy and K. J. Wirths, “Logarithmic coefficients and a coefficient conjecture for univalent functions,” Mon. Hefte Math., vol. 185, pp. 489-501. 2018.
  16. C. Pommerenke, Univalent Functions. Vanderhoeck and Ruprecht, Gottingen, Germany: Springer Science and Business Media, 1975.
  17. S. Ponnusamy, N. L. Sharma and K. J. Wirths, “Logarithmic coefficients problems in families related to starlike and convex functions,” J. Aust. Math. Soc., vol. 109, pp. 230-249. 2019.
  18. K. Sharma, N. K. Jain and V. Ravichandran, “Starlike functions associated with cardioid,” Afr. Mat., vol. 27, pp. 923-939. 2016.
  19. L. Shi, M. Arif, J. Iqbal, K. Ullah and S.M. Ghufran, “Sharp Bounds of Hankel Determinant on Logarithmic Coefficients for Functions Starlike with Exponential Function,” Fractal Fract., vol. 6, pp. 645. 2022.
  20. Y. J. Sim, A. Lecko and D. K. Thomas, “The second Hankel determinant for strongly convex and Ozaki close-to-convex functions,” Ann. Mat. Pura Appl., vol. 200, pp. 2515-2533. 2021.
  21. S. S. Kumar, G. Kamaljeet, “A cardioid domain and starlike functions,” Anal. Math. Phys., vol. 11, pp. 54. 2021.
  22. S. N. Malik, M. Raza, Q. Xin, J. Sokol, R. Manzoor, et al, “On Convex Functions Associated with Symmetric Cardioid Domain,” Symmetry, vol. 13, pp. 2321. 2021.
  23. B. Rath, D. V. Krishna, K. S. Kumar, and G. K. S. Viswanadh, “The sharp bound of the third Hankel determinants for inverse of starlike functions with respect to symmetric points”, Mat. Stud., vol. 58, no. 1, pp. 45-50. 2022.
  24. B. Rath, K. S. Kumar, and D. V. Krishna, “An exact estimate of the third Hankel determinants for functions inverse to convex functions”, Mat. Stud., vol. 60, no. 1, pp. 34-39. 2023.
  25. P. Sharma, R. K. Raina and J. Sokół, “Certain Ma–Minda type classes of analytic functions associated with the crescentshaped region,” Anal. Math. Phys., vol. 9, pp. 1887-1903. 2019.
  26. J. Sokół, D. K. Thomas, “The second Hankel determinant for alpha-convex functions,” Lith. Math. J., vol. 58, pp. 212-218. 2018.
  27. H. M. Srivastava, S. Sümer Eker, B. Seker and B. Çekiç, “Second Hankel Determinant of Logarithmic Coefficients for a subclass of univalent functions,” Miskolc Math. Notes., vol. 25, pp. 479-488. 2024.
  28. H. M. Srivastava, Q. Z. Ahmad, M. Darus, N. Khan, B. Khan, et al, “Upper bound of the third Hankel determinant for a subclass of close-to-convex functions associated with the lemniscate of Bernoulli,” Mathematics, vol. 7, pp. 1-10. 2019.
  29. L. Shi, H. M. Srivastava, M. Arif, S. Hussain and H. Khan, “An investigation of the third Hankel determinant problem for certain subfamilies of univalent functions involving the exponential unction,” Symmetry, vol. 11, pp. 1-14. 2019.
  30. S. Sümer Eker, B. Seker, B. Çekiç and M. Acu, “Sharp Bounds for the Second Hankel Determinant of Logarithmic Coefficients for Strongly Starlike and Strongly Convex functions,” Axioms, vol. 11, pp. 1-14. 2022.
  31. S. Sümer Eker, A. Lecko, B. Çekiç and B. Seker, “The Second Hankel Determinant of Logarithmic Coefficients for Strongly Ozaki Close-to-Convex Functions,” Bull. Malays. Math. Sci. Soc., vol. 46, pp. 1-23. 2023.
  32. L. A. Wani, A. Swaminathan, “Starlike and convex functions associated with a Nephroid domain,” Bull. Malays. Math. Sci. Soc., vol. 44, pp. 79–104. 2021.
  33. P. Zaprawa, “Initial logarithmic coefficients for functions starlike with respect to symmetric points,” Bol. Soc. Mat. Mex., vol. 27, pp. 1-13. 2021.