Abstract
Let 𝒮ℋ denote the class of functions f=h+g¯ that are harmonic univalent and sense-preserving in the unit disk U={z:|z|<1}, where h(z)=z+∑k=2∞akzk, g(z)=∑k=1∞bkzk(|b1|<1). In this paper, we introduce the class Mℋ(n,λ,α) of functions f=h+g¯ which are harmonic in U. A sufficient coefficient of this class is determined. It is shown that this coefficient bound is also necessary for the class Mℋ¯(n,λ,α) if fn(z)=h+gn¯∈Mℋ(n,λ,α), where h(z)=z−∑k=2∞|ak|zk, gn(z)=(−1)n∑k=1∞|bk|zk and n∈ℕ0. Coefficient conditions, such as distortion bounds, convolution conditions, convex combination, extreme points, and neighborhood for the class Mℋ¯(n,λ,α), are obtained.