Coefficient Conditions for Harmonic Close-to-Convex Functions

Abstract

New sufficient conditions, concerned with the coefficients of harmonic functions 𝑓(𝑧)=ℎ(𝑧)+𝑔(𝑧) in the open unit disk 𝕌 normalized by 𝑓(0)=ℎ(0)=ℎ(0)−1=0, for 𝑓(𝑧) to be harmonic close-to-convex functions are discussed. Furthermore, several illustrative examples and the image domains of harmonic close-to-convex functions satisfying the obtained conditions are enumerated.