Abstract
Let T be a nonexpansive mapping on a strictly convex and smooth Banach space X. It is shown, that T(ty)=ty for any t ε R implies T(x+y)=(Tx)+y for any x ε X.
Heisenberg Fellow of Deutsche Forschungsgemeinschaft
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
U. Krengel, M. Lin, An integral representation of disjointly additive order preserving operators in L 1, Stochastic Anal. Appl. 6 (1988), 289–304.
M. Lin, R. Wittmann, Pointwise ergodic theorems for certain order preserving mappings in L 1, Proceedings Conference A.E. Convergence, Evanston, Il. 1989 (to appear).
S. Reich, Asymptotic behavior of contractions in Banach spaces, J. Math. Anal. Appl. 44 (1973), 57–70.
R. Wittmann, Hopf’s ergodic theorem for nonlinear operators, Math. Ann. 289 (1981), 239–253.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag
About this paper
Cite this paper
Wittmann, R. (1992). Fixed point rays of nonexpansive mappings. In: Krengel, U., Richter, K., Warstat, V. (eds) Ergodic Theory and Related Topics III. Lecture Notes in Mathematics, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097541
Download citation
DOI: https://doi.org/10.1007/BFb0097541
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55444-8
Online ISBN: 978-3-540-47076-2
eBook Packages: Springer Book Archive