Coefficient estimates for a class of analytic bi-univalent functions related to pseudo-starlike functions

Abstract

In this paper we introduce and investigate an interesting subclass LB h;ṗ. / of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class LB h;ṗ. /, we obtain estimates on the first two Taylor-Maclaurin coefficients a 2 and a 3. The results presented in this paper would generalize and improve some recent work of Joshi et al. [5].

On a subclass of bi-univalent functions associated with the q-derivative operator

“…Since then, various subclasses of the bi-univalent function class Σ were introduced. The estimates on the first two coefficients |a 2 | and |a 3 | in the TaylorMaclaurin series expansion (1.1) were found in several recent studies (see [8,9,16]) and still an interest to many researchers.…”

“…Quite a number of great mathematicians studied the concepts of q-derivative, for example by Gasper and Rahman [15], Aral et al [6] and many others (see [1][2][3][7][8][9][10][11][12][13][14]).…”

Fekete-Szegö problem and Second Hankel Determinant for a class of bi-univalent functions

“…For 0 ≦ β < 1, a function f ∈ σ is in the class S * σ (β) of bi-starlike functions of order β, or K σ (β) of bi-convex functions of order β if both f and its inverse map f −1 are, respectively, starlike or convex of order β. For a history and examples of functions which are (or which are not) in the class σ, together with various other properties of subclasses of bi-univalent functions one can refer [3,6,7,14,22,24,28,29].…”

Initial bounds for analytic and bi-univalent functions by means of (p,q)−Chebyshev polynomials defined by differential operator

“…Since then, there have been many researchers (see [2,5,6,7,11,12,14,15,13]) investigated several interesting subclasses of the class Σ and found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 |. In fact, its worth to mention that by making use of the Faber polynomial coefficient expansions Jahangiri, Jay M., and Samaneh G. Hamidi [8] have obtained estimates for the general coefficients |a n | for bi-univalent functions subject to certain gap series.…”