On a new subclass of bi-univalent functions defined by using Salagean operator

Abstract

In this manuscript, by using the Salagean operator, new subclasses of bi-univalent functions in the open unit disk are defined. Moreover, for functions belonging to these new subclasses, upper bounds for the second and third coefficients are found.

On new subclasses of bi-univalent functions defined by generalized Sălăgean differential operator

“…Let the function f (z) given by (1.1) be in the class H m;n;1 ( ) = H m;n ( ) 0 < 1; m; n 2 N 0 ; m > n . Then ja 2 in the Theorem 3.1 we arrive at the following result given by[10].…”

A new general subclass of analytic bi-univalent functions

“…where the function g is given by (1.2). Theorem 1.3 (see [5]) Let the function f (z) given by (1.1) be in the class…”

“…In the light of the work by Şeker [5], we investigate the coefficient problem for functions f ∈ A given by (1.1) belonging to the bi-univalent function class B m,n,γ Σ (h, p) introduced in Definition 4 and give coefficient bounds on |a 2 | and |a 3 | . We obtain the improvements of results obtained by Şeker [5] given in Theorems 1.2 and 1.3 as a result of our main theorem (Theorem 2.1).…”

“…Very recently, Şeker [5] introduced the two subclasses of the bi-univalent function class Σ in Definitions 2 and 3 by using the Sălăgean differential operator and obtained nonsharp bounds on |a 2 | and |a 3 | for functions f ∈ Σ in each of these subclasses.…”

Coefficient estimates for families of bi-univalent functions defined by Ruscheweyh derivative operator

“…We indicate by Σ the family of bi-univalent functions in U given by (1). In fact, Srivastava et al [22] have actually revived the study of holomorphic and bi-univalent functions in recent years, it was followed by such works as those by Frasin and Aouf [8], Murugusundaramoorthy et al [13], Srivastava and Wanas [25] and others (see, for example [1,3,4,5,9,10,11,12,15,16,17,18,19,20,21,23,14,24,26,27,28,29,30,31,32,33]). We notice that the family Σ is not empty.…”