Research

Journal of Inequalities and Applications

, 2013:281

Open Access This content is freely available online to anyone, anywhere at any time.

Bounds for the second Hankel determinant of certain univalent functions

  • See Keong LeeAffiliated withSchool of Mathematical Sciences, Universiti Sains Malaysia Email author 
  • , V RavichandranAffiliated withDepartment of Mathematics, University of Delhi
  • , Shamani SupramaniamAffiliated withSchool of Mathematical Sciences, Universiti Sains Malaysia

Abstract

The estimates for the second Hankel determinant http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2013-281/MediaObjects/13660_2012_729_IEq1_HTML.gif of the analytic function http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2013-281/MediaObjects/13660_2012_729_IEq2_HTML.gif  , for which either http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2013-281/MediaObjects/13660_2012_729_IEq3_HTML.gif or http://static-content.springer.com/image/art%3A10.1186%2F1029-242X-2013-281/MediaObjects/13660_2012_729_IEq4_HTML.gif is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike and lemniscate starlike functions are obtained.

MSC: 30C45, 30C80.