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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 553381
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Abstract: It is shown that nonlinear operators which preserve the integral are order preserving if and only if they are nonexpansive in $ {L^1}$ and that those which commute with translation by a constant are order preserving if and only if they are nonexpansive in $ {L^\infty }$. Examples are presented involving partial differential equations, difference approximations and rearrangements.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0553381-X
PII: S 0002-9939(1980)0553381-X
Keywords: Nonlinear operator, order preserving, nonexpansive, rearragement
Article copyright: © Copyright 1980 American Mathematical Society