Faber Polynomial Coefficient Estimates of Bi-Close-to-Convex Functions Associated with Generalized Hypergeometric Functions

Abstract

A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric functions defined in Δ={z∈C:|z|<1} is introduced. The estimates for the general Taylor–Maclaurin coefficients of the functions in the introduced subclass are obtained by making use of Faber polynomial expansions. In particular, several previous results are generalized.

New Applications of Faber Polynomial Expansion for Analytical Bi-Close-to-Convex Functions Defined by Using q-Calculus

“…Motivated by the recent studies involving Faber polynomial expansion [52][53][54][55], the general coefficient |a j | of bi-close-to-convex functions of class C Σ (m, α, q) are determined using the Faber polynomial expansions in this study under suitable gap series conditions. After this, we demonstrate the unpredictable behaviour of initial coefficients |a 2 |, |a 3 | and investigate the Fekete-Szegő problem a 3 − a 2 2 .…”

Estimating the Second Order Hankel Determinant for the Subclass of Bi-Close-to-Convex Function of Complex Order

“…Srivastava et al [34] applied the Faber polynomial expansion method to estimate the coefficient of general Taylor-Maclaurin series and the Fekete-Szegö type inequalities for the class of bi-close-to-convex function. A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric functions, q-fractional derivative operator and with bounded boundary rotation is recently studied by [6,36] and coefficient estimates of bi-close-to-convex functions associated with generalized hypergeometric functions for Faber polynomial were studied by Jie et al [41].…”

Second Hankel Determinant for a New Subclass of Bi-Univalent Functions Related to the Hohlov Operator

“…In [3], Brannan and Taha obtained the non-sharp estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 | of S * Σ (α) and C Σ (α). Recently, many scholars have defined various subclasses of bi-univalent functions (see [4][5][6][7][8][9][10][11][12]) and investigated the non-sharp estimates of the first two coefficients of the Taylor-Maclaurin series expansion.…”