(P,Q)-Lucas polynomial coefficient inequalities of the bi-univalent function class
(P,Q)-Lucas polynomial coefficient inequalities of the bi-univalent function class
Recently, Lucas polynomials and other special polynomials gained importance in the field of geometricfunction theory. In this study, by connecting these polynomials, subordination, and the Al-Oboudi differential operator,we introduce a new class of bi-univalent functions and obtain coefficient estimates and Fekete–Szegö inequalities for thisnew class.
___
- [1] Al-Oboudi FM. On univalent functions defined by a generalized Sălăgean operator. International Journal of Mathematics
and Mathematical Science 2004 (27): 1429-1436.
- [2] Altınkaya Ş, Yalçın S. On the (p, q)-Lucas polynomial coefficient bounds of the bi-univalent function class. Boletín
de la Sociedad Matemática Mexicana 2019: 1-9.
- [3] Duren PL. Univalent Functions. Grundlehren der Mathematischen Wissenschaften. New York, NY, USA: Springer,
1983.
- [4] Filipponi P, Horadam AF. Derivative sequences of Fibonacci and Lucas polynomials. In: Bergum, GE, Philippou
AN, Horadam AF (editors). Applications of Fibonacci Numbers, Vol. 4. Dordrecht, the Netherlands: Kluwer
Academic Publishers; 1991, pp. 99-108.
- [5] Filipponi P, Horadam AF. Second derivative sequences of Fibonacci and Lucas polynomials. Fibonacci Quarterly
1993; 31 (3): 194-204.
- [6] Lee G, Asci M. Some properties of the (p, q) -Fibonacci and (p, q) -Lucas polynomials. Journal of Applied Mathematics
2012; 2012: 264842.
- [7] Lewin M. On a coefficient problem for bi-univalent functions. Proceedings of the American Mathematical Society
1967; 18 (1): 63-68.
- [8] Lupas A. A guide of Fibonacci and Lucas polynomials. Octagon Mathematics Magazine 1999; 7 (1): 2-12.
- [9] Salagean GS. Subclasses of univalent functions. In: Cazacu CA, Boboc N, Jurchescu M, Suciu I (editors). Complex
Analysis—Fifth Romanian-Finnish Seminar. Berlin, Heidelberg: Springer, 1983, pp. 363-372.