A Generalized Class of Univalent Harmonic Functions Associated with a Multiplier Transformation

Abstract

We define a new subclass of univalent harmonic mappings using multiplier transformation and investigate various properties like necessary and sufficient conditions, extreme points, starlikeness, radius of convexity. We prove that the class is closed under harmonic convolutions and convex combinations. Finally, we show that this class is invariant under Bernandi-Libera-Livingston integral for harmonic functions.

Keywords

• harmonic mapping
• convolution
• bernardi operator
• coefficient conditions
• extreme points