2013/02/23 by Sumit Nagpal, Nagpal, Sumit, V. Ravichandran +1
Computer Science · Mathematics · #30C45 #31A05 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CV #msc:30C45 #msc:31A05
paper · pdf · doi:10.48550/arxiv.1302.5791
arxiv created 2013/02/23 · openalex publication_date 2013/02/23 · arxiv updated 2013/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H denote the class of all complex-valued harmonic functions f in the open unit disk normalized by f(0)=0=fz(0)-1=f_z(0), and let A be the subclass of H consisting of normalized analytic functions. For ϕ∈ A, let WH-(ϕ):=\f=h+g ∈ H:h-g=ϕ\ and WH+(ϕ):=\f=h+g ∈ H:h+g=ϕ\ be subfamilies of H. In this paper, we shall determine the conditions under which the harmonic convolution f1*f2 is univalent and convex in one direction if f1 ∈ WH-(z) and f2 ∈ WH-(ϕ). A similar analysis is carried out if f1 ∈ WH-(z) and f2 ∈ WH+(ϕ). Examples of univalent harmonic mappings constructed by way of convolution are also presented.