2018/07/31 by Subzar Beig, Beig, Subzar, V. Ravichandran +1
Mathematics · #30C45 #31A05 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Inequalities and Applications
paper · pdf · doi:10.48550/arxiv.1807.11658
openalex publication_date 2018/07/31 · openalex created_date 2020/12/21 · openalex updated_date 2026/07/28
For k=1,2, let fk=hk+gk be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination f=ηf1+(1-η)f2 =ηh1+(1-η)h2 +η g1+(1-η)g2 and the combination f=ηh1+(1-η)h2+ηg1+(1-η)g2. For real η, the two mappings f and f are the same. We investigate the univalence and directional convexity of f and f for η∈ℂ. Some sufficient conditions are found for convexity of the combination f.