Uniform boundedness principle for non-linear operators on cones of functions

TL;DR

This paper establishes a uniform boundedness principle for a class of non-linear operators acting on cones of functions, focusing on their Lipschitz seminorms, with broad applicability to various non-linear operator classes.

Contribution

It introduces a new uniform boundedness principle specifically for non-linear operators on cones of functions, extending classical linear results to non-linear settings.

Findings

Proves a uniform boundedness principle for Lipschitz seminorms of non-linear operators.

Applicable to various classes of non-linear operators.

Provides a theoretical foundation for analyzing non-linear operator behavior.

Abstract

We prove an uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically non-linear operators.