Subclasses of Analytic Functions Subordinated to the Four-Leaf Function

Abstract

The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass A4r,s of analytic functions related to the four-leaf domain, to increase the adaptability of our investigation. The initial findings are the bound estimates for the coefficients |an|, n=2,3,4,5, among which the bound of |a2| is sharp. Also, we include the sharp-function illustration. Additionally, we obtain the upper-bound estimate for the second Hankel determinant for this subclass as well as those for the Fekete–Szegő functional. Finally, for these subclasses, we provide an estimation of the Krushkal inequality for the function class A4r,s.

Keywords

• analytic functions
• subordination
• four-leaf function
• coefficient inequalities
• Hankel determinant
• Fekete–Szegő functional