Certain New Families for Bi-Univalent Functions Defined by a Known Operator (original) (raw)

Coefficient Related Studies for New Classes of Bi-Univalent Functions

Mathematics

Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor–Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients a 2 , a 3 and a 4 of the functions in the newly defined classes are given. Obtaining Fekete–Szegő inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete–Szegő functional is obtained for each of the three classes.

New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems

2018

Inspired by the recent works of Srivastava et al. (2010), Frasin and Aouf (2011), and Caglar et al. (2013), we introduce and investigate in the present paper two new general subclasses of the class consisting of normalized analytic and bi-univalent functions in the open unit disk U. For functions belonging to these general subclasses introduced here, we obtain estimates on the Taylor-Maclaurin coefficients |a_2| and |a_3|. Several connections to some of the earlier known results are also pointed out. The results presented in this paper would generalize and improve those in related works of several earlier authors.

Coefficient estimates for a certain subclass of analytic and bi-univalent functions

Applied Mathematics Letters, 2012

In this paper, we introduce and investigate an interesting subclass H h,p Σ of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class H h,p Σ , 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 Srivastava et al.

On Certain Classes of Analytic and Univalent Functions Based on Al-Oboudi Operator

Bonfring

Following the works of [2, 4, 7, 9] of analytic and univalent functions in this paper we introduce two new classes etc., We have obtained coefficient estimates, growth & distortion theorems, extremal properties for these two classes. The determination of extreme points of a family of univalent functions leads to solve many extremal points.