Hankel Determinant for a Subclass of Starlike Functions with Respect to Symmetric Points Subordinate to the Exponential Function

Abstract

Let Ss*(ez) denote the class of starlike functions with respect to symmetric points subordinate to the exponential function, i.e., the functions which satisfy in the unit disk U the condition 2zf′(z)f(z)−f(−z)≺ez(z∈U). We obtained the sharp estimate of the second-order Hankel determinants H2,3(f) and improved the estimate of the third-order H3,1(f) for this functions class Ss*(ez).

Keywords

• analytic function
• starlike functions with respect to symmetric points
• Hankel determinant
• exponential function