Abstract.
We discuss Halpern’s convergence for nonexpansive mappings in Hilbert spaces. We prove that one of the conditions in [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. (Basel), 58 (1992), 486–491] is the weakest sufficient condition among the conditions known to us. We also improve a necessary condition, which is close to Wittmann’s. This is one step to solve the problem raised by Reich in 1974 and 1983.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
The author is supported in part by Grants-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology.
Received: 15 July 2008
Rights and permissions
About this article
Cite this article
Suzuki, T. Reich’s problem concerning Halpern’s convergence. Arch. Math. 92, 602–613 (2009). https://doi.org/10.1007/s00013-009-2945-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-009-2945-4