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Applicable Analysis
An International Journal
Volume 94, 2015 - Issue 6
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Articles

Metric regularity of a positive order for generalized equations

Pages 1270-1287 | Received 08 Jul 2013, Accepted 27 May 2014, Published online: 02 Jul 2014
 

Abstract

This paper focuses on the metric regularity of a positive order for generalized equations. More concretely, we establish verifiable sufficient conditions for a generalized equation to achieve the metric regularity of a positive order at its a given solution. The provided conditions are expressed in terms of the Fréchet coderivative/or the Mordukhovich coderivative/or the Clarke one of the corresponding multifunction formulated the generalized equation. In addition, we show that such sufficient conditions turn out to be also necessary for the metric regularity of a positive order of the generalized equation in the case where the multifunction established the generalized equation is closed and convex.

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Acknowledgements

The author would like to thank the editor and the referees for their helpful comments and suggestions.

Additional information

Funding

This research was funded by Vietnam National Foundation for Science and Technology (NAFOSTED).

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