International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 27, Pages 1751-1754
doi:10.1155/S0161171203204087
An application of a subordination chain
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148, Punjab 106, India
Received 12 April 2002
Copyright © 2003 Sukhjit Singh and Sushma Gupta. 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
Let K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol “≺” stands for
subordination.