Coefficient Estimates for Certain Classes of Bi-Univalent Functions

Abstract

A function analytic in the open unit disk D is said to be bi-univalent in D if both the function and its inverse map are univalent there. The bi-univalency condition imposed on the functions analytic in D makes the behavior of their coefficients unpredictable. Not much is known about the behavior of the higher order coefficients of classes of bi-univalent functions. We use Faber polynomial expansions of bi-univalent functions to obtain estimates for their general coefficients subject to certain gap series as well as providing bounds for early coefficients of such functions.

Faber polynomial coefficient estimates for certain classes of bi-univalent functions defined by using the Jackson (p,q)-derivative operator

“…In the literature, there are only a few works determining the general coefficient bounds |a n | for the analytic bi-univalent functions ( [7,16,18]). …”

Coefficient Bounds for Certain Subclasses ofm-Fold Symmetric Biunivalent Functions

“…Not much is known about the bounds on general coefficient | | for ≥ 4. In the literature, only few works determine general coefficient bounds | | for the analytic biunivalent functions (see [16][17][18]). The coefficient estimate problem for each of | | ( ∈ N \ {1, 2}; N = {1, 2, 3, .…”

Coefficient estimates for a certain class of analytic and bi-univalent functions defined by fractional derivative

“…where a 1 = 1 and the sum is taken over all nonnegative integers μ 1 , ..., μ n satisfying the following conditions: [1] and [2]; see also [17,8]). The first and the last polynomials are: D 1 n = a n D n n = a n 1 = 1.…”

“…In fact, the aforecited work of Srivastava et al [18] essentially revived the investigation of various sublasses of the bi-univalent function class Σ in recent years; it was followed by such works as those by Ali et al [3], Srivastava et al [17], Jahangiri and Hamidi [8] (see also [7,14,5,13] and the references cited in each of them).…”