Geometric Properties of the m-Leaf Function and Connected Subclasses

In this study, we introduce and explore the properties of the m-leaf function Qm defined in the open unit disk D, where m∈N, and this function is defined by the relation Qm(z):=1+m+1m+2z+1m+2zm+1. We determine the main geometrical characterization of this function, focusing on its univalency and its sharp bounds for the real and imaginary modulus. Also, we find radius of convexity, and we give a subordination and inclusion result. Using this function, we introduce a new subclass of analytic functions normalized as usual in D denoted by Amr,s, and an investigation of this class reveals some interesting properties.