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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 4732704, 11 pages
http://dx.doi.org/10.1155/2016/4732704
Research Article

Research on Geometric Mappings in Complex Systems Analysis

1College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan 466001, China
2College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050016, China

Received 16 June 2016; Accepted 1 November 2016

Academic Editor: Allan C. Peterson

Copyright © 2016 Yanyan Cui et al. 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

We mainly discuss the properties of a new subclass of starlike functions, namely, almost starlike functions of complex order , in one and several complex variables. We get the growth and distortion results for almost starlike functions of complex order . By the properties of functions with positive real parts and considering the zero of order , we obtain the coefficient estimates for almost starlike functions of complex order on . We also discuss the invariance of almost starlike mappings of complex order on Reinhardt domains and on the unit ball in complex Banach spaces. The conclusions contain and generalize some known results.