On ratios of certain analytic functions

Let H(z) = f(z) /g(z) and h(z) = f'(z) / g'(z) where bath f and g are in one of the classes whose  members are convex, starlike relative to the origin, or typicallyreal in the open unit disk E. Sharp bounds on   ∝ and gt; 0 and β and gt; 0 such that Re {H(z) } ∝ and gt; 0,  Re {h (z) } β and gt; 0, z ∈ E, are obtained with one exception. In the case where h( z) is considered for f and g typically-real, z is restricted to the precise region in E of univalence of the class of typically-real functions.

• Autores: Burdick, G. R.; Merkes, E. P.
• Tipo de recurso: Article of journal
• Fecha de publicación: 1975
• Institución: Universidad Nacional de Colombia
• Repositorio: Universidad Nacional de Colombia
• Idioma: spa
• OAI Identifier: oai:repositorio.unal.edu.co:unal/42390
• Acceso en línea: https://repositorio.unal.edu.co/handle/unal/42390; http://bdigital.unal.edu.co/32487/
• Palabra clave: Analytic functions; members are convex; class of typically-real functions
• Rights: openAccess
• License: Atribución-NoComercial 4.0 Internacional