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

Abstract

The motivation of the present article is to define the (p−q)-Wanas operator in geometric function theory by the symmetric nature of quantum calculus. We also initiate and explore certain new families of holormorphic and bi-univalent functions AE(λ,σ,δ,s,t,p,q;ϑ) and SE(μ,γ,σ,δ,s,t,p,q;ϑ) which are defined in the unit disk U associated with the (p−q)-Wanas operator. The upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szegö-type inequalities for the functions in these families are obtained. Furthermore, several consequences of our results are pointed out based on the various special choices of the involved parameters.

The study of coefficient estimates and Fekete–Szegö inequalities for the new classes of m-fold symmetric bi-univalent functions defined using an operator

“…Hence it is obvious that such inequalities were obtained regarding bi-univalent functions too and very recently published papers can be cited to support the assertion that the topic still provides interesting results [2,6,41]. Inspiring new results emerged when quantum calculus was involved in the studies, as can be seen in many papers [30] and in studies published very recently [5,12,17,39]. Some elements of the (p, q)-calculus must be used for obtaining the original results contained in this paper.…”

The Study of the New Classes of m-Fold Symmetric bi-Univalent Functions

“…The Fekete-Szegö problem is the problem of maximizing the absolute value of the functional |a 3 − µa 2 2 |. Fekete-Szegö inequalities for different classes of functions are studied in the papers [8][9][10][11][12][13][14].…”

“…Many authors obtained coefficient estimates of bi-univalent functions in the articles [2,[14][15][16][17][18][19][20][21][22][23][24][25].…”

Coefficient estimate of Bi-Univalent Function with respect to symmetric points Associated with Balancing Polynomials

“…Researchers were concerned about several classes of univalent functions [12,13,14,15] due to the Fekete-Szegö problem, proposed in 1933 [16] ; therefore, it stands to reason that similar inequalities were also discovered for bi-univalent functions, and fairly recent publications can be cited to back up the claim that the subject still yields intriguing findings [17,18,19] Because of their importance in probability theory, mathematical statistics, mathematical physics, and engineering, orthogonal polynomials have been the subject of substantial research in recent years from a variety of angles. The classical orthogonal polynomials are the orthogonal polynomials that are most commonly used in applications (Hermite polynomials, Laguerre polynomials, Jacobi polynomials, and Bernoulli).…”