On relations between the classes S and U

Article Type

Research Article

Publication Title

Journal of Analysis

Abstract

Let A denote the family of all functions f analytic in the unit disk D and satisfying the normalization f(0) = 0 = f′(0) - 1. Let S denote the subclass of A consisting of univalent functions in D. We consider the subclass U of S that is defined by the condition that for its members f the condition |(zf(z))2f′(z)-1|<1forz∈Dholds. To these relations belong striking similarities and on the other hand big differences. We show that some results about S can be improved for U, while others cannot.

First Page

83

Last Page

93

DOI

10.1007/s41478-016-0023-4

Publication Date

6-1-2016

Link to Full Text

Share

COinS