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On the problem of Gromova and Vasil'ev on integral means, and Yamashita's conjecture for spirallike functions
Date Issued
01-01-2014
Author(s)
Indian Institute of Technology, Madras
Wirths, Karl Joachim
Abstract
In this article we consider some integral means problem for certain classes of univalent analytic functions, in particular for the class of the starlike functions of order β and for the class of α-spirallike functions of order β. Our investigation settles one of the open problems of Gromova and Vasil'ev. In addition, we solve another problem concerning area maximum property of α-spirallike functions of order β in the setting of Yamashita and hence, we find the solution to Yamashita's conjecture for certain Dirichlet-finite functions in a general form.
Volume
39