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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 892641, 7 pages
http://dx.doi.org/10.1155/2014/892641
Research Article

Implicit Multifunction Theorems in Banach Spaces

1School of Management, Fudan University, Shanghai 200433, China
2Department of Mathematics, Luoyang Normal University, Luoyang, Henan 471022, China

Received 31 December 2013; Accepted 21 January 2014; Published 9 March 2014

Academic Editor: Nan-Jing Huang

Copyright © 2014 Ming-ge Yang and Yi-fan Xu. 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

This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property, nonemptiness, and lower semicontinuity of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Ekeland variational principle, the Clarke subdifferential, and the Clarke coderivative.