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Journal of Function Spaces
Volume 2018, Article ID 6783748, 5 pages
https://doi.org/10.1155/2018/6783748
Research Article

Uniform Boundedness Principle for Nonlinear Operators on Cones of Functions

1Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, SI-1000 Ljubljana, Slovenia
2Institute of Mathematics, Physics and Mechanics, Jadranska 19, SI-1000 Ljubljana, Slovenia

Correspondence should be addressed to Aljoša Peperko; is.jl-inu.sf@okrepep.asojla

Received 29 December 2017; Revised 7 March 2018; Accepted 15 March 2018; Published 23 April 2018

Academic Editor: Adrian Petrusel

Copyright © 2018 Aljoša Peperko. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove a 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 nonlinear operators.