On metric subregularity for set-valued mappings under additive perturbations

In this paper, we derive new sufficient conditions together with the moduli estimation for metric subregularity of sum mappings consisting of a set-valued mapping and a continuous but possibly nonsmooth single-valued additive part. The obtained results address subregularity simultaneously in three d...

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Bibliographic Details
Published in:Applicable analysis Vol. 104; no. 18; pp. 3687 - 3716
Main Authors: Ouyang, Wei, Zhang, Binbin, Zhu, Jiangxing
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 12.12.2025
Taylor & Francis Ltd
Subjects:
Banach spaces
coderivative
error bound
Mapping
Metric subregularity/regularity
Perturbation
Stability
subdifferential
ISSN:0003-6811, 1563-504X
Online Access:Get full text
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Summary:In this paper, we derive new sufficient conditions together with the moduli estimation for metric subregularity of sum mappings consisting of a set-valued mapping and a continuous but possibly nonsmooth single-valued additive part. The obtained results address subregularity simultaneously in three different settings: general Banach spaces, Asplund spaces, and an Asplund pre-image space and a Banach image space with a norm which is Fréchet differentiable at nonzero points. We show that the stability of metric subregularity property under additive small perturbations by a smooth, or Lipschitz continuous, or specific type of nondifferentiable single-valued mapping, respectively, is equivalent. Finally, we establish some conditions for the stability of error bound property and metric regularity as applications.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2025.2505614