Author:
Alazman Ibtehal,Ibrahim Rabha W.
Abstract
In this effort, we present a new definition of the Steiner symmetrization by using special analytic functions in a complex domain (the open unit disk) with respect to the origin. This definition will be used to optimize the class of univalent analytic functions. Our method is based on the concept of differential subordination and the Carathéodory theory. Examples are illustrated in the sequel involving the modified Libera–Livingston–Bernardi integral operator over the open unit disk. The result gives that this integral satisfies the definition of bounded turning function (univalent analytic function).
Reference5 articles.
1. Planar poincar domains: geometry and Steiner symmetrization;Smith;J Anal Mathm,1995
2. Applications of Steiner symmetrization to some extremal problems in geometric function theory;Peretz;arXiv preprint arXiv:1607.01674,2016
3. Some extremal problems for certain families of analytic functions I;Janowski;Annales Polonici Mathematici,1973
4. Differential Subordinations
5. Conformal capacity of hedgehogs;Betsakos;Confor Geom Dyn Am Mathem Soc,2023