Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions

Abstract

In this work, considering a general subclass of analytic bi-univalent functions, we determine estimates for the general Taylor-Maclaurin coecients of the functions in this class. For this purpose, we use the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

“…Equation 23in conjunction with (24) would readily yield (17). We next solve (20) for a 3 , take the absolute values and apply Lemma 2.…”

Certain classes of bi-univalent functions with bounded boundary variation

“…Various subclasses of the bi-univalent function class Σ were introduced and non-sharp estimates on the first two coefficients |a 2 | and |a 3 | in the Taylor-Maclaurin series expansion (1.1) were found in several recent investigations (see, for example, [1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,29,30,31,32,33,34,35] and references therein). The aforecited all these papers on the subject were actually motivated by the pioneering work of Srivastava et al [28].…”

Coefficient Estimates for a Certain General Subclass of Analytic and Bi-Univalent Functions

“…So we get the desired estimate on 2 a as asserted in (1.5). Next, in order to find the bound on 3 a , by subtracting (1.10) from (1.8), we get ( ) ( ) [4]. Similarly, various other interesting corollaries and consequences of our main result can be derived by choosing different ϕ and ψ .…”