A class of harmonic starlike functions defined by multiplier transformation

Abstract

We define two new subclasses, HS(k, λ, b, α) and HS(k, λ, b, α), of univalent harmonic mappings using multiplier transforma-tion. We obtain a sufficient condition for harmonic univalent functions to be in HS(k, λ, b, α) and we prove that this condition is also necessary for the functions in the class HS(k, λ, b, α). We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class HS(k, λ, b, α).