Horadam polynomials and their applications to new family of bi-univalent functions with respect to symmetric conjugate points
DOI:
https://doi.org/10.22199/issn.0717-6279-2021-01-0007Keywords:
Bi-univalent functions, Horadam polynomials, Upper bounds, Symmetric conjugate, Fekete-Szegö problem, SubordinationAbstract
In the current paper, by making use of the Horadam polynomials, we introduce and investigate a new family of holomorphic and biunivalent functions with respect to symmetric conjugate points defined in the open unit disk D. We derive upper bounds for the second and third coefficients and solve Fekete-Szegö problem of functions belongs to this family.
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References
E. A. Adegani, S. Bulut, and A. A. Zireh, ”Coefficient estimates for a subclass of analytic bi-univalent functions”, Bulletin Korean Mathematical Society, vol. 55, no. 2, pp. 405-413, 2018, doi: 10.4134/BKMS.b170051
Ş. Altınkaya and S. Yalçın, ”On the Chebyshev coefficients for a general subclass of univalent functions”, Turkish journal of mathematics, vol. 42, no. 6, pp. 2885-2890, 2018, doi: 10.3906/mat-1510-53
Ş. Altınkaya and S. Yalçın, ”On the Chebyshev polynomial coefficient problem of some subclasses of bi-univalent functions”, Gulf journal of mathematics, vol. 5, no. 3, pp. 34-40, 2017. [On line]. Available: https://bit.ly/2JOLqwa
S. Bulut, ”Coefficient estimates for general subclasses of m-fold symmetric analytic bi-univalent functions”, Turkish journal of mathematics, vol. 40, no. 6, pp. 1386-1397, 2016, doi: 10.3906/mat-1511-41.
P. L. Duren, Univalent functions. New York, NY: Springer, 1983.
R. M. El-Ashwah and D. K. Thomas, “Some subclasses of close-to-convex functions”, Journal of the Ramanujan Mathematical Society, vol. 2, no. 1, pp. 86-100, 1987. [On line]. Available: https://bit.ly/3bm41eF
A. F. Horadam, “Jacobsthal representation polynomials”, The Fibonacci quarterly, vol. 35, no.2, pp. 137-148, 1997. [On line]. Available: https://bit.ly/2L1Slmy
A. F. Horadam and J. M. Mahon, “Pell and Pell-Lucas polynomials”, The Fibonacci quarterly, vol. 23, no. 1, pp. 7-20, 1985. [On line]. Available: https://bit.ly/2XeKfJC
T. Horzum and E. G. Kocer, “On some properties of Horadam polynomials”, International mathematical forum, vol. 4, no. 25, pp. 1243- 1252, 2009. [On line]. Available: https://bit.ly/3npQHYS
T. Koshy, Fibonacci and Lucas numbers with applications. New York, NY: A Wiley-Interscience, 2001, doi: 10.1002/9781118033067
A. Lupas, “A Guide of Fibonacci and Lucas polynomials”, Octagon mathematics magazine, vol. 7, no. 1, pp. 2-12, 1999.
S. S. Miller and P. Mocanu, Differential subordinations: theory and applications. New York, NY: Marcel Dekker, 2000.
H. M. Srivastava, S¸. Altınkaya, and S. Yalçın, ”Certain subclasses of bi-univalent functions associated with the Horadam polynomials”, Iranian journal of science and technology, transactions A: Science, vol. 43, pp. 1873-1879, 2019, doi: 10.1007/s40995-018-0647-0
H. M. Srivastava, S. S. Eker, S. G. Hamidi, and J. M. Jahangiri, ”Faber polynomial coefficient estimates for bi-univalent functions defined by the Tremblay fractional derivative operator”, Bulletin Iranian Mathematical Society, vol. 44, no. 1, pp. 149-157, 2018, doi: 10.1007/s41980- 018-0011-3
H. M. Srivastava, S. Gaboury, and F. Ghanim, “Coefficient estimates for some general subclasses of analytic and bi-univalent functions”, Afrika matematika, vol. 28, pp. 693-706, 2017, doi: 10.1007/s13370-016-0478-0
H. M. Srivastava, A. K. Mishra, and P. Gochhayat, “Certain subclasses of analytic and Bi-Univalent functions”, Applied mathematics letters, vol. 23, pp. 1188-1192, 2010, doi: 10.1016/j.aml.2010.05.009
H. M. Srivastava and A. K. Wanas, “Initial Maclaurin coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination”, Kyungpook Mathematical Journal, vol. 59, no. 3, pp. 493-503, 2019, doi: 10.5666/KMJ.2019.59.3.493
A. K. Wanas and A. L. Alina, “Applications of Horadam polynomials on Bazilevič bi-univalent function satisfying subordinate conditions”, Journal of physics: conference series, vol. 1294, no. 3, Art ID. 032003, 2019 doi: 10.1088/1742-6596/1294/3/032003
A. K. Wanas and S. Yalçın, “Initial coefficient estimates for a new subclasses of analytic and m-Fold symmetric bi-univalent functions”, Malaya journal of matematik, vol. 7, no. 3, pp. 472-476, 2019, doi: 10.26637/MJM0703/0018
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