The Pre-Schwarzian Norm Estimate for Analytic Concave Functions

Young Jae Sim and Oh Sang Kwon

International Journal of Mathematics and Mathematical Sciences, 2015, vol. 2015, 1-6

Abstract:

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.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:814805

DOI: 10.1155/2015/814805

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