New classes of analytic and bi-univalent functions

Abstract

<abstract><p>Using the (p, q)-derivative operator we introduce new subclasses of analytic and bi-univalent functions, we obtain estimates on coefficients and the Fekete-Szegö functional.</p></abstract>

Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (p − q)-Wanas Operator

“…In fact, Srivastava et al [2] have actually revived the study of analytic and bi-univalent functions in the recent years. This was followed by works such as those by Frasin and Aouf [3], Ali et al [4], Bulut et al [5], Srivastava and et al [6] and others (see, for example, [7][8][9][10][11][12][13][14][15]).…”

“…In [8], the authors obtained Fekete-Szegö inequalities for classes of analytic and bi-univalent functions defined by (p, q)-derivative operator; 3.…”

Applications of (M,N)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions

“…There have been many papers in recent years on analytic and bi-univalent functions, e.g., [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

“…Its origin is in the disproof by Fekete and Szegö in [1] of the Littlewood-Paley conjecture that the coefficients of odd univalent functions are bounded by unity. The Fekete-Szegö problem has been studied in recent years for many classes of univalent functions, see, for example: [2][3][4][5][6][8][9][10][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Best Dominants and Subordinants for Certain Sandwich-Type Theorems

“…There are many results concerning the theory of differential subordination and superordination techniques involving differential operators and integral operators as we can mention here [8]. For special function see [9]. Definition 1.…”