Coefficient bounds for certain subclasses of bi-univalent functions

Abstract

Abstract. In this paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions. Also, we find estimates of |a 2 | and |a 3 |. Some related consequences of the results are also pointed out. Mathematics Subject Classification: 30C45

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

“…For a brief history of functions in the class, see [27] (see also [9,10,20,22]). Recently, Srivastava et al [27], Altınkaya and Yalçın [6], and Magesh and Yamini [21] made an effort to introduce various subclasses of the bi-univalent function class Σ and found non-sharp coefficient estimates on the initial coefficients |a 2 | and |a 3 | (see also [28]). But the coefficient problem for each one of the following Taylor-Maclaurin coefficients…”

Coefficients Bounds for Certain Subclass of Biunivalent Functions Associated with Ruscheweyh q-Differential Operator

“…Brannan and Taha [5] introduced certain subclass of the biunivalent functions class Σ. For a brief history and interesting examples of biunivalent functions we refer to [3,[5][6][7][8][9][10][11].…”

Certain Subclasses of Bistarlike and Biconvex Functions Based on Quasi-Subordination

“…For a brief history and interesting examples of functions which are in (or which are not in) the class , together with various other properties of the biunivalent function class , one can refer to the work of Srivastava et al [6] and references therein. Recently, various subclasses of the biunivalent function class were introduced and nonsharp estimates on the first two coefficients | 2 | and | 3 | in the Taylor-Maclaurin series expansion (1) were found in several recent investigations (see, e.g., [7][8][9][10][11][12][13][14][15][16][17]). But the problem of finding the coefficient bounds on | | ( = 3, 4, .…”