Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47H15, 47H10

Retrieve articles in all journals with MSC: 47H15, 47H10


Additional Information

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