Some Further Coefficient Bounds on a New Subclass of Analytic Functions

Abstract

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass SQ of analytic functions with f′(z) subordinated to 1/(1−z)2 in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant H2,3f and the third Hankel determinant H3,1f for f∈SQ. This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions.

Keywords

• subordination
• analytic functions
• Hankel determinant
• coefficient bounds