International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 205845, 19 pages
http://dx.doi.org/10.1155/2011/205845
Research Article

Differential Subordinations of Arithmetic and Geometric Means of Some Functionals Related to a Sector

A. Lecko1 and M. Lecko2

1Department of Analysis and Differential Equations, University of Warmia and Mazury in Olsztyn, Street Zolnierska 14, 10-561 Olsztyn, Poland
2Department of Mathematics, Rzeszów University of Technology, Street W. Pola 2, 35-959 Rzeszów, Poland

Received 30 December 2010; Accepted 30 March 2011

Academic Editor: Hans Keiding

Copyright © 2011 A. Lecko and M. Lecko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Some general theorems on differential subordinations of some functionals connected with arithmetic and geometric means related to a sector are proved. These results unify a number of well known results concerning inclusion relation between the classes of analytic functions built with using arithmetic and geometric means.