PreprintCC BY 4.0arXiv
Mordukhovich Derivatives and Covering Constant for Set-Valued Metric Projection in General Banach Spaces
Abstract
In this paper, we find the explicit representation of the set-valued metric projection operator from l1 to the unit closed ball in l1. By using this representation, we investigate the properties of the Mordukhovich derivatives of the set-valued metric projection operator, which is applied to calculate its covering constant. As a special case, we consider the 2-d Banach space. We find the explicit solutions of the set-valued metric projection operator from the considered 2-d Banach space to its unit closed ball. By these solutions, we will calculate its Mordukhovich derivatives in details.
Related
- Some Properties of Mordukhovich Derivatives with Applications to Locally Variational Inequalities in Banach Spaces
- P-adic Curved Kakeya Sets, Projection Theorem and Covering Numbers
- An exact hierarchy for Lebesgue's universal covering constant and a certified 0.834 lower bound
- A non-lattice periodic point set beating the optimal lattice packing-covering constant in dimension five
- Prescribed projections for a general class of maps and efficient covering by variable plane curves
BibTeX
@misc{li2026mordukhovich,
title = {{Mordukhovich Derivatives and Covering Constant for Set-Valued Metric Projection in General Banach Spaces}},
author = {Jinlu Li},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28961},
eprint = {2608.28961},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28961},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mordukhovich Derivatives and Covering Constant for Set-Valued Metric Projection in General Banach Spaces
AU - Jinlu Li
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.28961
UR - https://arxiv.org/abs/2608.28961
AB - In this paper, we find the explicit representation of the set-valued metric projection operator from l1 to the unit closed ball in l1. By using this representation, we investigate the properties of the Mordukhovich derivatives of the set-valued metric projection operator, which is applied to calculate its covering constant. As a special case, we consider the 2-d Banach space. We find the explicit solutions of the set-valued metric projection operator from the considered 2-d Banach space to its unit closed ball. By these solutions, we will calculate its Mordukhovich derivatives in details.
ER -