2013/06/23 by Sushma Gupta, Kumar, Raj, Gupta, Sushma +5
Mathematics · #30C45 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:30C45
paper · pdf · doi:10.48550/arxiv.1306.5375
8 pages
arxiv created 2013/06/23 · openalex publication_date 2013/06/23 · arxiv updated 2013/06/25 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
Dorff et al. [4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping fβ= hβ+ gβ, where fβis obtained by shearing of analytic vertical strip mapping, with dilatation eiθzn; n = 1,2,θ∈ R, is in SH0 and is convex in the direction of the real axis. In this paper, by using Cohn's rule, we generalize this result by considering dilatations (a-z)/(1-az), a∈ (-1,1) and eiθ zn (n∈ N;θ∈ R) of right half-plane mapping and fβ, respectively.