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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 3512326, 14 pages
Research Article

Geometric Mappings under the Perturbed Extension Operators 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
3Institute of Contemporary Mathematics, Henan University, Kaifeng, Henan 475001, China

Correspondence should be addressed to Yanyan Cui

Received 3 March 2017; Accepted 8 May 2017; Published 15 June 2017

Academic Editor: Chris Goodrich

Copyright © 2017 Chaojun Wang 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.


In this paper, we mainly seek conditions on which the geometric properties of subclasses of biholomorphic mappings remain unchanged under the perturbed Roper-Suffridge extension operators. Firstly we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Secondly, applying the analytical characteristics and growth results of subclasses of biholomorphic mappings, we conclude that the generalized Roper-Suffridge operators preserve the geometric properties of strong and almost spiral-like mappings of type and order , as well as almost spiral-like mappings of type and order under different conditions on Bergman-Hartogs domains. Sequentially we obtain the conclusions on the unit ball and for some special cases. The conclusions include and promote some known results and provide new approaches to construct biholomorphic mappings which have special geometric characteristics in several complex variables.