Error bounds for vector-valued funtions on metric spaces
- Authors: Kruger, Alexander , Bednarczuk, Ewa
- Date: 2012
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics Vol. 40, no. 2/3 (2012), p. 165-180
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- Description: In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new primal space derivative-like objects – slopes – are introduced and a classification scheme of error bound criteria is presented.
Slopes of multifunctions and extensions of metric regularity
- Authors: Ngai, Huynh Van , Kruger, Alexander , Thera, Michel
- Date: 2012
- Type: Text , Journal article
- Relation: Vietnam Journal of Mathematics (Tạp chí toán học) Vol. 40, no. 2/3 (2012), p. 355-369
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: This article aims to demonstrate how the definitions of slopes can be extended to multi-valued mappings between metric spaces and applied for characterizing metric regularity. Several kinds of local and nonlocal slopes are defined and several metric regularity properties for set-valued mappings between metric spaces are investigated.