Nonlinear metric regularity on fixed sets

Abstract

The aim of this paper is to study some new models of nonlinear regularity on fixed sets of set-valued mappings defined on the complete metric spaces. Slope and coderivative characterizations of these models are given. The stability of the Milyutin regularity is investigated when the initial set-valued mapping is perturbed by a suitable Lipschitz single-valued map.

Keywords:

• Nonlinear regularity
• Milyutin regularity
• slope
• coderivative
• perturbation stability

2020 Mathematics Subject Classifications:

• 49J52
• 49J53
• 90C30

Acknowledgements

We are grateful to the two referees. Their reports are so much helpful for us to improve the quality of the manuscript in the aspect of mathematics as well as the one of language, and both in the presentation. We also would like to thank one of the referees to mention the papers [48,61] which are very useful for us. We would like to thank VINIF for this support.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research is supported by VINIF (Vingroup Innovation Foundation) under grant VINIF.2019.DA09.