On the uniform convexity of the squared distance
Metric Geometry
2025-12-12 v2 Optimization and Control
Abstract
In 1983, Z\u{a}linescu showed that the squared norm of a uniformly convex normed space is uniformly convex on bounded subsets. We extend this result to the metric setting of uniformly convex hyperbolic spaces. We derive applications to the convergence of shadow sequences and to proximal minimization.
Keywords
Cite
@article{arxiv.2503.03442,
title = {On the uniform convexity of the squared distance},
author = {Andrei Sipos},
journal= {arXiv preprint arXiv:2503.03442},
year = {2025}
}