Applications of Horadam Polynomials for Bi-univalent Functions associated with Gamma-Starlike Function
DOI:
https://doi.org/10.29304/jqcsm.2024.16.41802Keywords:
Horadam Polynomials, Gamma-Starlike Functions, Coefficient bounds, Subordination, Bi-univalent functionAbstract
This study presents a novel subclass of analytic and bi-univalent functions within the open unit disk, utilizing Horadam polynomials related to Gamma-starlike functions. Our primary focus is on deriving upper bounds for the second and third Taylor-Maclaurin coefficients of functions belonging to this subclass. We employ subordination techniques and properties of Horadam polynomials to establish these coefficient estimates.
Downloads
References
S. Altinkaya and S. Yalcin, "Coefficient bounds for a subclass of bi-univalent functions," TWMS Journal of Pure and Applied Mathematics, vol. 6, pp. 180-185, 2015.
S. Altinkaya and S. Yalcin, "Faber Polynomial coefficient bounds for a subclass of bi-univalent functions," C. R. Acad. Sci. Paris, Ser. I., vol. 353, pp. 1075-1080, 2015.
S. Altinkaya and S. Yalcin, "On a new subclass of bi-univalent functions satisfying subordinate conditions," Acta Universitatis Sapientiae, Mathematica, vol. 7, pp. 5-14, 2015.
W. G. Atshan, S. Yalcin, and R. A. Hadi, "Coefficients estimates for special subclass of k-fold symmetric bi-univalent functions," Mathematics for Applications, vol. 9, no. 2, pp. 83-90, 2020.
M. Caglar, H. Orhan, and N. Yagmur, "Coefficient bounds for new subclasses of bi-univalent functions," Filomat, vol. 27, pp. 1165–1171, 2013.
M. Darus and D. K. Thomas, "Inverse coefficients of α-logarithmically convex functions," Jnanabha, vol. 45, pp. 31–36, 2015.
E. Deniz, "Certain subclasses of bi-univalent functions satisfying subordinate conditions," J. Classical Anal., vol. 2, no. 1, pp. 49-60, 2013.
P. Duren, "Subordination," in Complex Analysis, vol. 599 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977, pp. 22-29.
B. A. Frasin and M. K. Aouf, "New subclasses of bi-univalent functions," Appl. Math. Lett., vol. 24, pp. 1569-1573, 2011.
S. G. Hamidi and J. M. Jahangiri, "Faber polynomial coefficient estimates for analytic bi-close to convex functions," C. R. Acad. Sci. Paris, Ser. I., vol. 352, pp. 17-20, 2014.
A. F. Horadam and J. M. Mahon, "Pell and Pell-Lucas polynomials," Fibonacci Quart., vol. 23, pp. 7-20, 1985.
T. Hörcum and E. G. Kocer, "On some properties of Horadam polynomials," Int. Math. Forum, vol. 4, pp. 1243-1252, 2009.
Z. Lewandowski, S. S. Miller, and E. Zlotkiewicz, "Gamma-starlike functions," Ann. Univ. Marie Curie-Sklodowska, vol. 28, pp. 32-36, 1974.
W. Ma and D. Minda, "Unified treatment of some special classes of univalent functions," in Proceedings of the Conference on Complex Analysis, Z. Li, F. Ren, L. Yang, and S. Zhang, Eds., Int. Press, 1992, pp. 157-169.
Q. A. Shakir, A. S. Tayyah, D. Breaz, L.-I. Cotîrlă, Rapeanu, E., and F. M. Sakar, "Upper bounds of the third Hankel determinant for bi-univalent functions in crescent-shaped domains," Symmetry, vol. 16, 1281, 2024.
Q. A. Shakir and W. G. Atshan, "On third Hankel determinant for certain subclass of bi-univalent functions," Symmetry, vol. 16, 239, 2024.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Hayder Kadim Mohammed
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.