On metric subregularity for set-valued mappings under additive perturbations - Ouyang, Wei; Zhang, Binbin; Zhu, Jiangxing (Applicable analysis, 2025)
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.