Journal of Applied Mathematics
Volume 2012 (2012), Article ID 682465, 12 pages
http://dx.doi.org/10.1155/2012/682465
Research Article

Global Dynamical Systems Involving Generalized 𝑓 -Projection Operators and Set-Valued Perturbation in Banach Spaces

Yun-zhi Zou,1 Xi Li,2 Nan-jing Huang,2 and Chang-yin Sun1

1School of Automation, Southeast University, Jiangsu, Nanjing 210096, China
2Department of Mathematics, Sichuan University, Sichuan, Chengdu 610064, China

Received 29 February 2012; Accepted 16 May 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Yun-zhi Zou 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

A new class of generalized dynamical systems involving generalized f-projection operators is introduced and studied in Banach spaces. By using the fixed-point theorem due to Nadler, the equilibrium points set of this class of generalized global dynamical systems is proved to be nonempty and closed under some suitable conditions. Moreover, the solutions set of the systems with set-valued perturbation is showed to be continuous with respect to the initial value.