2014/07/10 by Swadesh Kumar Sahoo, Sahoo, Swadesh Kumar
Mathematics · #30C20 #30C35 #51M16 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1407.2753
openalex publication_date 2014/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider ordinary derivative of universal covering mappings\nf of hyperbolic regions D in the complex plane. We obtain sharp bounds for\nthe ratio |f'(z)|/ rm dist(f(z),\∂ f(D)) in terms of the hyperbolic\ndensity in simply connection domains. In arbitrary domains, we find a necessary\nand sufficient condition for an upper bound for the quantity |f'(z)|/ rm\ndist(f(z),\∂ f(D)) to hold in terms of the hyperbolic density. As an\napplication of the above results, it is observed that the bounds for the\nquantity of the above type are closely connected with similar bounds for\n|f''(z)/f'(z)|.\n