Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of the Noor integral operator
Inclusion properties of Lucas polynomials for bi-univalent functions introduced through the q-analogue of the Noor integral operator
In this paper, by using the (P; Q) -Lucas polynomials and the q-analogue of the Noor integral operator, weaim to build a bridge between the theory of geometric functions and that of special functions.
___
- [1] Akgül A. Coefficient estimates for certain subclass of bi-univalent functions obtained with polylogarithms. Mathematical
Sciences and Applications E-Notes 2018; 6: 70-76.
- [2] Akgül A, Altınkaya Ş. Coefficient estimates associated with a new subclass of bi-univalent functions. Acta Universitatis
Apulensis 2017; 52: 121-128.
- [3] Altınkaya Ş, Yalçın S. Faber polynomial coefficient bounds for a subclass of bi-univalent functions. C R Acad Sci
Paris Ser I 2015; 353: 1075-1080.
- [4] Altınkaya Ş, Yalçın S. On the certain subclasses of univalent functions associated with the Tschebyscheff polynomials.
Transylvanian Journal of Mathematics and Mechanics 2016; 8: 105-113.
- [5] Arif M, Ul Haq M, Liu J-L. Subfamily of univalent functions associated with q -analogue of Noor integral operator.
J Funct Spaces 2018; 2018: 3818915.
- [6] Brannan DA, Taha TS. On some classes of bi-univalent functions. Stud Univ Babeş-Bolyai Math 1986; 31: 70-77.
- [7] Fekete M, Szegö G. Eine Bemerkung über ungerade schlichte Funktionen. J London Math Soc 1933; 2: 85-89 (in
German).
- [8] Filipponi P, Horadam AF. Derivative sequences of Fibonacci and Lucas polynomials. Applications of Fibonacci
Numbers,1991; 4: 99-108.
- [9] Lee GY, Aşcı M. Some properties of the (p; q) -Fibonacci and (p; q) -Lucas polynomials. J Appl Math 2012; 2012:
1-18.
- [10] Lewin M. On a coefficient problem for bi-univalent functions. P Am Math Soc 1967; 18: 63-68.
- [11] Lupas A. A guide of Fibonacci and Lucas polynomials. Octagon Math Mag 1999; 7: 2-12.
- [12] Netanyahu E. The minimal distance of the image boundary from the origin and the second coefficient of a univalent
function in jzj < 1. Arch Ration Mech Anal 1969; 32: 100-112.
- [13] Noor KI. On new classes of integral operators. J Natur Geom 1999; 16: 71-80.
- [14] Sakar FM. Estimate for initial Tschebyscheff polynomials coefficients on a certain subclass of bi-univalent functions
defined by Salagean differential operator. Acta Universitatis Apulensis 2018; 54: 45-54.
- [15] Sakar FM. Estimating coefficients for certain subclasses of meromorphic and bi-univalent functions, Journal of
Inequalities and Applications 2018; 283: 1-8.
- [16] Srivastava HM. Univalent functions, fractional calculus, and associated generalized hypergeometric functions. In:
Srivastava HM, Owa S, editors. Univalent Functions; Fractional Calculus, and Their Applications. New York, NY,
USA: John Wiley and Sons, 1989.
- [17] Srivastava HM, Mishra AK, Gochhayat P. Certain subclasses of analytic and bi-univalent functions. Appl Math
Lett 2010; 23: 1188-1192.
- [18] Vellucci P, Bersani AM. The class of Lucas-Lehmer polynomials. Rend Math Appl 2016; 37: 43-62.
- [19] Wang T, Zhang W. Some identities involving Fibonacci, Lucas polynomials and their applications. Bull Math Soc
Sci Math Roum 2012; 55: 95-103.