English

Inclusion Criteria for Subclasses of Functions and Gronwall's Inequality

Complex Variables 2011-08-30 v1

Abstract

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 α\alpha-Bazilevi\^c of order β\beta.

Keywords

Cite

@article{arxiv.1108.5421,
  title  = {Inclusion Criteria for Subclasses of Functions and Gronwall's Inequality},
  author = {Rosihan M. Ali and Mahnaz M. Nargesi and V. Ravichandran and A. Swaminathan},
  journal= {arXiv preprint arXiv:1108.5421},
  year   = {2011}
}