Stable classes of harmonic mappings

Let H0 denote the set of all sense-preserving harmonic mappings f=h+g‾ in unit disk D, normalized with h(0)=g(0)=g′(0)=0 and h′(0)=1. In this paper, we mainly investigate some properties certain subclasses H0, including inclusion relations stability analysis by precise examples, coefficient bounds, growth, covering distortion theorems. As applications, build Bohr inequalities for these means subordination. Among subclasses, six classes consist functions f=h+g‾∈H0 such that h+ϵg is univalent (or convex) D each |ϵ|=1 |ϵ|=1, or |ϵ|≤1). Simple shows if function belongs to a given class from classes, then h+ϵg‾ belong corresponding |ϵ|=1. We call as stable classes.