The Hartman-Stampacchia Theorem and the Maximum Displacements of Nonvanishing Continuous Vector-Valued Functions
Functional Analysis
2025-02-04 v1
Abstract
This paper aims at giving solutions to six interesting interconnected open questions suggested by Professor Biagio Ricceri. The questions focus on the behavior of nonvanishing continuous vector-valued functions in finite-dimensional normed spaces as well as in infinite-dimensional normed spaces. Using the celebrated Hartman-Stampacchia Theorem (1966) on the solution existence of variational inequalities, we establish sharp lower estimates for the maximum displacements of nonvanishing continuous vector-valued functions. Then, combining the obtained results with suitable tools from functional analysis and several novel geometrical constructions, we get the above-mentioned solutions.
Keywords
Cite
@article{arxiv.2502.00746,
title = {The Hartman-Stampacchia Theorem and the Maximum Displacements of Nonvanishing Continuous Vector-Valued Functions},
author = {Nguyen Nang Thieu and Nguyen Dong Yen},
journal= {arXiv preprint arXiv:2502.00746},
year = {2025}
}