Inclusion Criteria for Subclasses of Functions and Gronwall's Inequality

Details Inclusion Criteria for Subclasses of Functions and Gronwall's Inequality Inclusion Criteria for Subclasses of Functions and Gronwall's Inequality

2011-08-27

arxiv.org/abs/1108.5421v1

Mathematics

Complex Variables

Scientific paper

A normalized analytic function f is shown to be univalent in the open unit disk D if its second coefficient is sufficiently small and relates to its Schwarzian derivative through a certain inequality. New criteria for analytic functions to be in certain subclasses of functions are established in terms of the Schwarzian derivatives and the second coefficients. These include obtaining a sufficient condition for functions to be strongly $\alpha$-Bazilevi\^c of order $\beta$.

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