Coefficient Conditions for Harmonic Close-to-Convex Functions

Abstract

New sufficient conditions, concerned with the coefficients of harmonic functions $f\left(z\right)=h\left(z\right)+\overline{g\left(z\right)}$ in the open unit disk $𝕌$ normalized by $f\left(0\right)=h\left(0\right)=h^{\prime }\left(0\right)-1=0$, for $f\left(z\right)$ 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.