Two Families of Bi-Univalent Functions Associating the (p, q)-Derivative with Generalized Bivariate Fibonacci Polynomials - Sondekola Rudra Swamy; Basem Aref Frasin; Daniel Breaz; Luminita-Ioana Cotîrlă (Mathematics)
Making use of generalized bivariate Fibonacci polynomials, we propose two families of regular functions of the type <semantics>ϕ(ζ)=ζ+<mstyle displaystyle="true"><munderover>∑j=2∞</munderover></mstyle>djζj</semantics>, which are bi-univalent in the disc <semantics>{ζ∈C:|ζ|<1}</semantics> involving the (p, q)-derivative operator. We find estimates on the coefficients <semantics>|d2|</semantics>, <semantics>|d3|</semantics> and the of Fekete–Szegö functional for members of these families. Relevant connections to the existing results and new consequences of the main result are presented.