(P,Q)-Lucas polynomial coefficient inequalities of the bi-univalent function class

Abstract

Recently, Lucas polynomials and other special polynomials gained importance in the field of geometric function theory. In this study, by connecting these polynomials, subordination, and the Al-Oboudi differential operator, we introduce a new class of bi-univalent functions and obtain coefficient estimates and Fekete-Szegö inequalities for this new class.

Applications Laguerre Polynomials for Families of Bi-Univalent Functions Defined with (p,q)-Wanas Operator

“…Later, such studies continued by Ali et al [3], Bulut et al [4], Srivastava et al [5] and others (see, for example, [6][7][8][9][10][11][12][13][14][15][16][17][18]). However, non decisive predictions of the |a 2 | and |a 3 | coefficients in given by (1) were declared in different studies.…”

Bi-univalent functions of order ζ connected with ( m , n ) -Lucas polynomials

“…Depending on the values of m and n, some special polynomials can be obtained from the (m, n)-Lucas polynomial like the Lucas polynomials L x,1,j (x), the Pell-Lucas polynomials L 2x,1,j (x), the Jacobsthal polynomials L 1,2x,j (x), the Fermat-Lucas polynomials L 3x,−2,j (x), and the first-kind Chebyshev polynomials L 2x,−1,j (x). Many authors have provided studies on the (m, n)-Lucas polynomial ( [1,7,[39][40][41]).…”

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

“…The (M, N)-Lucas Polynomial has been presented and investigated analogously by various classes of functions (see, for example [32,[60][61][62][63][64][65]).…”