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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Generic properties of contraction semigroups and fixed points on nonexpansive operators

Authors: F. S. De Blasi and J. Myjak
Journal: Proc. Amer. Math. Soc. 77 (1979), 341-347
MSC: Primary 47H15; Secondary 47H10
MathSciNet review: 545593
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Abstract: Let $ \Omega $ be a nonempty, closed, bounded and starshaped subset of a Banach space X. It is shown that most (in the Baire category sense) differential equations $ u' + Au = 0$ do have a unique asymptotic equilibrium point. Here $ A:\Omega \to X$ is supposed to be a nonlinear, continuous, bounded and accretive operator satisfying the Nagumo boundary condition. An application to the fixed point theory of nonexpansive operators $ F:\Omega \to X$ satisfying $ F(\partial \Omega ) \subset \Omega $ is given.

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Keywords: Differential equation, asymptotic equilibrium, contraction semigroup, nonexpansive mapping, fixed point, Baire category, residual set, generic property, accretive operator, Nagumo boundary condition
Article copyright: © Copyright 1979 American Mathematical Society

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