Generic properties of contraction semigroups and fixed points on nonexpansive operators

De Blasi, F. S.; Myjak, J.

doi:10.1090/S0002-9939-1979-0545593-8

Generic properties of contraction semigroups and fixed points on nonexpansive operators
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by F. S. De Blasi and J. Myjak

Proc. Amer. Math. Soc. 77 (1979), 341-347

DOI: https://doi.org/10.1090/S0002-9939-1979-0545593-8

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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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