No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Coefficient estimates for a subclass of analytic functions using Faber polynomials
Abstract
In this paper, we introduce and investigate a new subclass Q^{∗∗}_{Σ }(α, ϕ) of normalized analytic functions defined using convolution in the open unit disk U whose inverse has univalent analytic continuation to U. Estimates of the coefficients of biunivalent functions belonging to this class are determined by using Faber polynomial
techniques.
... In 1967, the class of bi-univalent functions was constructed by Lewin [7] and the second coefficient for functions belonging to this class as | 2 | < 1.51 was estimated.Brannan and Clunie [2]improved his result to| 2 | ≤ √2. There aremany theories on the estimates of the initial coefficients of bi-univalent functions [1,3,4,5,6,8,[10][11][12][13][14][15][16]. ...
... By using (12) in (15) ...
In this paper, a newsubclass of bi-univalent functions using (p,q) −Chebyshev polynomials was constructed by the authors. Initially, the bounds for the first two coefficients viz., |a2|, |a3| were obtained. Finally, Fekete-Szegö inequalitywas calculated.
Nous exprimons les coefficients des développements de fonctions analytiques bi-presque convexes en utilisant les polynômes de Faber, et nous en déduisons des estimations de ces coefficients. Une fonction est dite bi-univalente dans un domaine si elle et son inverse sont univalentes dans ce domaine. Nous montrons également le comportement imprévisible des premiers coefficients pour des sous-classes de fonctions bi-univalentes.
Let S be the class of functions f which are analytic and univalent in the unit disc E with f ( 0 ) = 0 , f ′ ( 0 ) = 1 . Let C , S * and K be the classes of convex, starlike and close-to-convex functions respectively. The class C * of quasi-convex functions is defined as follows:
Let f be analytic in E and f ( 0 ) , f ′ ( 0 ) = 1 . Then f ϵ C * if and only if there exists a g ϵ C such that, for z ϵ E Re ( z f ′ ( z ) ) ′ g ′ ( z ) > 0 .
In this paper, an up-to-date complete study of the class C * is given. Its basic properties, its relationship with other subclasses of S , coefficient problems, arc length problem and many other results are included in this study. Some related classes are also defined and studied in some detail.
In this paper, a new class of normalized univalent functions is introduced. The properties of this class and its relationship with some other subclasses of univalent functions are studied. The functions in this class are close-to-convex.
Properties of the Grunsky coefficients and Schwarzian derivative associated with powers of a given series are examined.
This chapter discusses some classes of bi-univalent functions. It presents several classes of functions f(z) = z + ∑anzn that are analytic and univalent in the unit disc U = {z : | z | < l}. The class of all such functions is denoted by S. The σ denotes the class of all functions of the form f(z) = z + ∑anzn that are analytic and bi-univalent in the unit disc, that is, f ∈ S and f−1 has a univalent analytic continuation to {| w | < l}. The chapter also introduces the following classes: (1) the class S*σ [α] of strongly bi-starlike functions of order α, 0 < α ≤ 1; (2) the class S*σ(β) of bi-starlike functions of order β, 0 ≤ β < 1; and (3) the class Cσ(β) of bi-convex functions of order β, 0 ≤ β < 1.
With the differential calculus on the Faber polynomials, we calcu-late the Faber polynomials for powers of inverse functions. We apply the same methods to obtain majoration of the derivatives of the Faber polynomials of a univalent function of the class Σ.
Symmetric sums associated to the factorization of Grunsky co-109 efficients
- H Airault
H. Airault, Symmetric sums associated to the factorization of Grunsky co-109
efficients, in Conference, Groups and Symmetries, Montreal, Canada, April
110
2007.
Co-efficient estimates for the class of
- G Saravanan
- K Muthunagai
G. Saravanan and K. Muthunagai, Co-efficient estimates for the class of