文章基本信息

标题：The Pre-Schwarzian Norm Estimate for Analytic Concave Functions
本地全文：下载
作者：Young Jae Sim ; Oh Sang Kwon
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2015
卷号：2015
DOI：10.1155/2015/814805
出版社：Hindawi Publishing Corporation
摘要：Let denote the open unit disk and let denote the class of normalized univalent functions which are analytic in . Let be the class of concave functions , which have the condition that the opening angle of at infinity is less than or equal to , . In this paper, we find a sufficient condition for the Gaussian hypergeometric functions to be in the class . And we define a class , , which is a subclass of and we find the set of variabilities for the functional for . This gives sharp upper and lower estimates for the pre-Schwarzian norm of functions in . We also give a characterization for functions in in terms of Hadamard product.