Some relations between nonexpansive and order preserving mappings

Crandall, Michael G.; Tartar, Luc

doi:10.1090/S0002-9939-1980-0553381-X

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: 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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