On some classes of harmonic functions with conditions imposed on coefficients and their arguments

In this paper we consider a few classes of functions $f$ harmonic in the unit disc $\Delta$ of the form $f=h+\overline{g}$, where $h, g$ are suitably normalized functions holomorphic in $\Delta$. Our special attention is drawn to some classes generated by respective coefficient conditions and to classes of functions with conditions imposed on coefficient arguments. We examine relationships between these conditions and some analytic conditions of stalikeness or convexity of considered functions.