Initial Coefficient Estimates and Fekete–Szegö Inequalities for New Families of Bi-Univalent Functions Governed by (<i>p</i> − <i>q</i>)-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.

Keywords

• holormorphic function
• bi-univalent function
• upper bounds
• Fekete–Szegö functional
• (<i>p</i> − <i>q</i>)-Wanas operator