| Keywords and phrases: analytic functions, univalent and bi-univalent functions, Horadam polynomials, Borel distribution, coefficient bounds, subordination.
Received: October 1, 2021; Accepted: December 19, 2021; Published: February 8, 2022
How to cite this article: Adnan Ghazy Al Amoush, Initial coefficient bounds for certain families of bi-univalent functions involving the Borel distribution associated with Horadam polynomials, International J. Functional Analysis, Operator Theory and Applications 14 (2022), 1-12. DOI: 10.17654/0975291922001
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License  
References:
[1] A. Amourah, A. G. Alamoush and M. Al-Kaseasbeh, Gegenbauer polynomials and bi-univalent functions, Palestine J. Math. 10(2) (2021), 625-632.
[2] A. G. Alamoush, On subclass of analytic bi-close-to-convex functions, Int. J. Open Problems Complex Analysis 13(1) (2021), 11-18.
[3] A. G. Alamoush and M. Darus, Coefficient bounds for new subclasses of bi-univalent functions using Hadamard product, Acta Univ. Apulensis (2014), 153-161.
[4] A. G. Alamoush and M. Darus, On coefficient estimates for bi-univalent functions of Fox-Wright functions, Far East J. Math. Sci. (FJMS) 89(2) (2014), 249-262.
[5] A. G. Alamoush and M. Darus, On coefficient estimates for new generalized subclasses of bi-univalent functions, AIP Conference Proceedings 1614, 2014, pp. 844-850.
[6] A. G. Alamoush, On a subclass of bi-univalent functions associated to Horadam polynomials, Int. J. Open Problems Complex Analysis 12(1) (2020), 58-65.
[7] A. G. Alamoush, Certain subclasses of bi-univalent functions involving the Poisson distribution associated with Horadam polynomials, Malaya J. Matematik 7 (2019), 618-624.
[8] A. G. Alamoush, Coefficient estimates for a new subclass of lambda-pseudo bi-univalent functions with respect to symmetrical points associated with the Horadam polynomials, Turkish J. Math. 43 (2019), 2865-2875.
[9] A. G. Al Amoush and S. Bulut, On a subclass of bi-close-to-convex functions by means of the Gegenbauer polynomial, Math. Appl. 10 (2021), 93-101.
[10] A. F. Horadam and J. M. Mahon, Pell and Pell-Lucas Polynomials, The Fibonacci Quarterly (1985), 7-20.
[11] A. F. Horadam, Jacobsthal representation polynomials, The Fibonacci Quarterly (1997), 137-148.
[12] A. K. Wanas and A. G. Al Amoush, Applications of Borel distribution series on holomorphic and bi-univalent functions, Math. Morav. 25(2) (2021), 97-107.
[13] A. K. Wanas and J. A. Khuttar, Applications of Borel distribution series on analytic functions, Earthline J. Math. Sci. 4 (2020), 71-82.
[14] A. Lupas, A guide of Fibonacci and Lucas polynomials, Mathematics Magazine (1999), 2-12.
[15] Ş. Altinkaya and S. Yalçin, On the Chebyshev polynomial coefficient problem of bi-Bazilevic functions, Turkish World Math. Soc. J. Appl. Eng. Math. 10(1) (2020), 251-258.
[16] D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babeş-Bolyai Mathematicac 31(2) (1988), 70-77.
[17] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent function, Appl. Math. Lett. (2010), 1188-1192.
[18] H. M. Srivastava, G. Murugusundaramoorthy and K. Vijaya, Coefficient estimates for some families of bi-Bazilevič functions of the Ma-Minda type involving the Hohlov operator, J. Classical Anal. 2(2) (2013), 167-181.
[19] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amar. Math. Soc. (1967), 63-68.
[20] P. L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, NY, USA, 259, 1986.
[21] T. Horzum and E. G. Kocer, On some properties of Horadam polynomials, Int. Math. Forum 4 (2009), 1243-1252.
[22] T. Koshy, Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, 2001.
|
