Stability of random implicit multifunctions in separable Asplund spaces

Volume 10, Issue 4, pp 2241--2256 http://dx.doi.org/10.22436/jnsa.010.04.74

Publication Date: April 20, 2017 Submission Date: February 12, 2017

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Authors

Ming-ge Yang - School of Management, Shanghai University, Shanghai 200444, P. R. China. Yi-fan Xu - School of Management, Fudan University, Shanghai 200433, P. R. China.

Abstract

This paper is mainly devoted to present new sufficient conditions in terms of Fr´echet coderivatives for the local metric regularity, the metric regularity, the Lipschitz-like property, the nonemptiness and the lower semicontinuity of random implicit multifunctions in separable Asplund spaces. An example is given to illustrate the above random implicit multifunction results. Some applications to stability analysis of solution maps for random parametric generalized equations are also given.

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Keywords

• Fréchet coderivative
• random implicit multifunction
• (local) metric regularity
• Lipschitz-like property
• lower semicontinuity.

MSC

•  49J53
•  90C31

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