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

Abstract

With the aid of the q-binomial coefficients and utilizing the convolution, we define a new q-convolution operator that helps us introduce two new families of bi-univalent functions. These classes are connected by subordination with a function G m,n . We give upper bounds for the coefficients estimate |a j | (j = 2, 3) of the functions that belong to these families, followed by some special cases. Moreover, we found estimates for the Fekete-Szeg ö inequality for both of these families, followed by simple particular results. We emphasize that the defined convolution q-difference operator generalizes some other operators given by several authors. As an application of this study, Fekete-Szeg ö inequalities for these classes of functions defined by Pascal distribution are investigated.

The Yamaguchi–Noshiro Type of Bi-Univalent Functions Connected with the Linear q-Convolution Operator

“…In [16] (see also [2,10,[17][18][19][20][21][22][23][24][25][26]), certain subclasses of the bi-univalent analytic functions class B were introduced and non-sharp estimates on the first two coefficients |c 2 | and |c 3 | were found. The object of the present paper is to introduce two new subclasses as in Definitions 1 and 2 of the function class B using the linear q-convolution operator and determine estimates of the coefficients |c 2 |, |c 3 | and |c 4 | for the functions in these new subclasses of the function class B.…”

Exploring a Special Class of Bi-Univalent Functions: q-Bernoulli Polynomial, q-Convolution, and q-Exponential Perspective

“…Setting ω = τ, ζ = 1, υ = 0, and S n,1,0,q α,ρ,ω,ω , we obtain the operator defined by Hadi et al [40].…”