Firmly nonexpansive and Kirszbraun-Valentine extensions: a constructive approach via monotone operator theory

TL;DR

This paper introduces a new constructive method for extending firmly nonexpansive mappings and monotone operators, leveraging proximal-average techniques to provide a novel perspective on classical extension theorems.

Contribution

The paper presents a constructive approach to extending firmly nonexpansive mappings and monotone operators using proximal-average methods, offering new insights into classical extension results.

Findings

New constructive extension method for firmly nonexpansive mappings

Application of proximal-average techniques to classical theorems

Enhanced understanding of monotone operator extensions

Abstract

Utilizing our recent proximal-average based results on the constructive extension of monotone operators, we provide a novel approach to the celebrated Kirszbraun-Valentine Theorem and to the extension of firmly nonexpansive mappings.