Coefficient bounds for new subclasses of bi-univalent functions

Abstract

In the present paper, introduction of new subclasses of bi-univalent functions in the open disk was defined. Moreover,by using Salagean operator,in these new subclasses for functions, upper bounds for the second and third coefficients were found. Presented results are a generalization of the results obtained by Srivastava et al.[12], Frasin and Aouf [7] and Ç aglar et al.[5].

Certain subclasses of analytic functions and bi-univalent functions defined on the unite disc

“…A function f 2 A is said to be bi-univalent in E if f and f 1 are univalent in E. Let be the class of bi-univalent functions in E which is given by (1.1). Lewin [14] investigated the bi-univalent function class and showed that ja 2 j < 1:51: For an interesting examples and a brief history in the class ; see [15] ( see also [15,16,17,18,19,20,21,22,23,24]).…”

A Generalized Subclass of Alpha Convex Bi-Univalent Functions of Complex Order

“…They introduced bi-starlike functions and bi-convex functions and obtained estimates on the initial coefficients. Also the subclasses of bi-univalent functions defined by Salagean operator were studied by various authors [3,9,11,15].…”

Application of quasi-subordination for certain subclasses of bi-univalent functions of complex order

“…For a brief history and interesting examples in the class Σ, see [25] (see also [5], [6], [13], [16]). Furthermore, judging by the remarkable flood of papers on the subject (see, for example, [11], [23] and [24]). Not much is known about the bounds on the general coefficient |a n | .…”