On coefficient inequalities of certain subclasses of bi-univalent functions involving the Sălăgean operator

Abstract

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.

Coefficient Estimates and the Fekete–Szegö Problem for New Classes of m-Fold Symmetric Bi-Univalent Functions

“…Horadam polynomials were used for applications on Bazilevic bi-univalent functions satisfying subordination conditions [16] and for introducing certain classes of bi-univalent functions [17]. Operators were also included in the study as it can be seen in earlier publications [18] and in very recent ones [19]. In 2014, Srivastava et al [20] defined m-fold symmetric bi-univalent functions following the concept of m-fold symmetric univalent functions.…”

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

“…Horadam polynomials were used for applications on Bazilevic bi-univalent functions satisfying subordination conditions [40] and for introducing certain classes of bi-univalent functions [1]. Operators were also included in the study as it can be seen in earlier publications [9] and in very recent ones [28]. Interesting results regarding m-fold symmetric bi-univalent functions were published in the same year when this notion was introduced [21].…”