Some relations between nonexpansive and order preserving mappings

Authors:
Michael G. Crandall and Luc Tartar

Journal:
Proc. Amer. Math. Soc. **78** (1980), 385-390

MSC:
Primary 47H07

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553381-X

MathSciNet review:
553381

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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that nonlinear operators which preserve the integral are order preserving if and only if they are nonexpansive in and that those which commute with translation by a constant are order preserving if and only if they are nonexpansive in . Examples are presented involving partial differential equations, difference approximations and rearrangements.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0553381-X

Keywords:
Nonlinear operator,
order preserving,
nonexpansive,
rearragement

Article copyright:
© Copyright 1980
American Mathematical Society