Coefficient Estimate Problem for a New Subclass of Biunivalent Functions

Abstract

We introduce a unified subclass of the function class Σ of biunivalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients | 2 | and | 3 | for functions in this subclass. In addition, many relevant connections with known or new results are pointed out.

Certain classes of bi-univalent functions with bounded boundary variation

“…Various subclasses of the bi-univalent function class Σ were introduced and non-sharp estimates on the first two coefficients |a 2 | and |a 3 | in the Taylor-Maclaurin series expansion (1.1) were found in several recent investigations (see, for example, [1,2,4,5,6,7,8,10,11,12,13,14,15,16,17,19,21,22,23,24,25,26,27,29,30,31,32,33,34,35] and references therein). The aforecited all these papers on the subject were actually motivated by the pioneering work of Srivastava et al [28].…”

Bounds for Two New Subclasses of Bi-Univalent Functions Associated with Legendre Polynomials

“…Let σ be the class of all bi-univalent functions in U. Lewin [5] is the first author who introduced the class of analytic bi-univalent functions and estimated the second coefficient |a 2 |. Many authors created several subclasses of analytic bi-univalent functions and found the bounds for the first two coefficients |a 2 | and |a 3 | , see for example [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Let Ω be the class of all analytic functions ω in U which satisfy these conditions ω(0) = 0 and |ω(z)| < 1 for all z ∈ U.…”

Faber polynomials coefficients estimates for a certain subclass of Bazilevic functions

“…In 1967, Lewin [18] was the first author who studied the class of analytic and bi-univalent functions. Later, the first two coefficients |a 2 | and |a 3 | for different subclasses of analytic and bi-univalent functions were estimated by many authors, see for example [3,4,6,7,12,13,[15][16][17]19,20,[22][23][24]27,28]. In 1903, Faber [10] introduced Faber polynomials which have an effective role in some branches of mathematics.…”