Estimates for Coefficients of Bi-Univalent Functions Associated with a Fractional <i>q</i>-Difference Operator

Abstract

In the present paper, we discuss a class of bi-univalent analytic functions by applying a principle of differential subordinations and convolutions. We also formulate a class of bi-univalent functions influenced by a definition of a fractional q-derivative operator in an open symmetric unit disc. Further, we provide an estimate for the function coefficients |a2| and |a3| of the new classes. Over and above, we study an interesting Fekete–Szego inequality for each function in the newly defined classes.

Keywords

• differential subordination
• <i>q</i>-analogue
• difference operator
• coefficient estimates