Proceedings of the American Mathematical Society · 1980 · 52 citations · 3 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsFinite Element MethodsIntegral EquationsOperator TheoryMonotone MappingsMonotone Operator TheoryNonexpansive MappingsNonlinear Integral EquationsNonlinear Partial Differential EquationsOperator InequalitiesOperatorsOrder-preserving Maps
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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