How averaged is the projection?
Functional Analysis
2025-07-23 v2 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
Projection operators are important in Analysis, Optimization and Algorithm. It is well known that these operators are firmly nonexpansive. In this paper, we provide an exact result that sharpens this well-known result. We develop the theory of averaged operators and provide a lower bound. We give a result on the avergedness of operator compositions. We also provide some nonlinear examples to illustrate our results.
Keywords
Cite
@article{arxiv.2312.15421,
title = {How averaged is the projection?},
author = {Shuang Song},
journal= {arXiv preprint arXiv:2312.15421},
year = {2025}
}
Comments
This manuscript is not yet mature. A significantly revised and more complete version will be uploaded at a later date