(U, V) - LUCAS POLYNOMIAL AND BI-UNIVALENT FUNCTION

International Journal of Computer Science (IJCS) Published by SK Research Group of Companies (SKRGC)

Abstract

In this paper, by using Lucas polynomials, developed a new family of bi-univalent functions D_? (s,t,z). Also, obtained (U, V) - Lucas polynomial, coefficient estimates and Fekete -Szegö inequalities for this new class D_? (s,t,z). Mathematics Subject Classification 2010: 30C45.

References

1.  Aldawish, T. Al-Hawary and B. A. Frasin, Subclasses of bi-univalent functions defined by Frasin differential operator, Mathematics, 8 (2020), pp. 783.
2. S. Altinkaya and S. Yalçin, On the (p,q) Lucas polynomial coefficient bounds of the bi-univalent function class, Boletín de la Sociedad MatemÂt’atica Mexicana, 25 (2019), pp. 567–575.
3. S. Altinkaya and S. Yalçin, Coefficient estimates for two new subclasses of bi-univalent functions with respect to symmetric points, J. Funct. Spaces, (2015), pp. 1–5.
4. A. Amourah and M. Illafe, A Comprehensive subclass of analytic and Bi-univalent functions associated with subordination, Palestine Journal of Mathematics, 9(2020), pp. 187–193.
5. D. Brannan and J. Clunie, Aspects of contemporary complex analysis, Academic Press, New York, 1980.
6. D. Brannan and T. S. Taha, On some classes of bi-univalent functions, Mathematical Analysis and Its Applications (1988), pp. 53–60.
7. P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA, 1983.
8. M. Fekete and G. Szegö, Eine Bemerkung ber Ungerade Schlichte Funktionen, J. London Math. Soc., 1 (1933), pp. 85–89.
9. B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011), pp. 1569–1573.
10. B. A. Frasin And T. Al-Hawary, Initial Maclaurin coefficients bound for new subclasses of bi-univalent functions, Theory Appl. Math. Comp. Sci., 5 (2015), pp. 186–193.
11. G. Y. Lee and M. Asâÿcâÿä´s, Some properties of the (p q) Fibonacci and (p q) Luca’s polynomials, J. Appl. Math., 2012 (2012), pp. 1–18.
12. M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967), pp. 63–68.
13. H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23 (2010), pp. 1188–1192.
14. H. M. Srivastava, S. Bulut, Cm. Âÿag¸ Lar and N. Yag?mur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27 (2013), pp. 831–842.
15. P Vellucci and A. M. Bersani, The class of Lucasâ?A ¸SLehmer polynomials, Rend. Mat. Appl.serie VII, 37 (2016), pp. 43–62.
16. F. Yousef, T. Al-Hawary and G. Murugusundaramoorthy, Fekete-Szegö functional problems for some subclasses of bi-univalent functions defined by Frasin differential operator, Afr.Mat., 30 (2019), pp. 495–503.
17. F. Yousef, S. Alroud and M. Illafe, A comprehensive subclass of bi-univalent functions associated with Chebyshev polynomials of the second kind, Boletin de la Sociedad Matematica Mexicana (2019), pp. 1–11.
18. A. Zireh, E. Analouei Adegani and S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg.Math. Soc. Simon Stevin, 23 (2016), pp. 487–504.

Keywords

Analytic function, Bi-univalent function, Coefficient estimate, Lucas polynomial, Sakaguchi type function.