Application of Chebyshev polynomials to certain subclass of Non-Bazilevic functions

Abstract

In this paper, we introduce a new certain subclass N(α, λ, t) of Non-Bazilević analytic functions of type (1 − α) by using the Chebyshev polynomials expansions. We investigated some basic useful characteristics for this class, also we obtain coefficient bounds and Fekete-Szegö inequalities for functions belong to this class. This class is considered a general case for some of the previously studied classes. Further we discuss its consequences. which are analytic and univalent in the open unit disk U = {z : z ∈ C : |z| < 1}. Let S be the class of analytic functions f (z) ∈ A and normalized with the following conditions f (0) = 0 and f (0) = 1. Let f (z) and (z) are analytic functions in U, we say that the function f (z) is a subordinate to (z) in U, written as f (z) ≺ (z), if there exists a Schwarz function w(z), which is analytic in U with w(0) = 0 and |w(z)| < 1, (z ∈ U) such that f (z) = (w(z)). Furthermore, if (z) is univalent in U, then we have the following equivalent f (z) ≺ (z), (z ∈ U) ⇐⇒ f (0) = (0) and f (U) ⊂ (U). (see[7]) The Fekete-Szegö functional |a 3 − µa 2 2 | for normalized Taylor-Mclaurin series f (z) = z + a 2 z 2 + a 3 z 3 + ...

Estimates of Coefficient for Certain Subclasses of k-Fold Symmetric Bi-Univalent Functions

“…Many experiments have been conducted to investigate estimates 𝜅-fold bi-univalent functions with different subclasses, for detail [13][14][15][16][17][18][19]. The aim of this paper is to determine Taylor-Maclaurin coefficients and for functions belong to the a new subclasses .…”