Applications of the <i>q</i>-Derivative Operator to New Families of Bi-Univalent Functions Related to the Legendre Polynomials

Abstract

By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete–Szegö-type inequalities for functions in each of these subclasses are obtained. The results derived in this article are shown to extend and generalize those in some earlier works.

Keywords

• analytic functions
• bi-univalent functions
• q-derivative operator
• subordination between analytic functions
• Legendre polynomials
• Fekete–Szegö inequality