2021/03/18 by Mathi, Manivannan, Prajapat, Jugal Kishore
#30C45 #30C55 #31A05 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2103.10140
For α> -1 and β>0, let BH0(α, β) denote the class of sense preserving harmonic mappings f=h+g in the open unit disk \mathbbD satisfying |zh''(z)+α(h'(z)-1)|≤ β-|zg''(z)+αg'(z)|. First, we establish that each function belonging to this class is close-to-convex in the open unit disk if β∈ (0, 1+α]. Next, we obtain coefficient bounds, growth estimates and convolution properties. We end the paper with applications and will construct harmonic univalent polynomials belonging to this class.