An Upper Bound of the Third Hankel Determinant for a Subclass of <i>q</i>-Starlike Functions Associated with <i>k</i>-Fibonacci Numbers

Abstract

In this paper, we use q-derivative operator to define a new class of q-starlike functions associated with k-Fibonacci numbers. This newly defined class is a subclass of class A of normalized analytic functions, where class A is invariant (or symmetric) under rotations. For this function class we obtain an upper bound of the third Hankel determinant.

Keywords

• starlike functions
• subordination
• <i>q</i>-Differential operator
• <i>k</i>-Fibonacci numbers