Vol. 60, No. 2, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 311: 1
Vol. 310: 1  2
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Fixed point iterations of nonexpansive mappings

Simeon Reich

Vol. 60 (1975), No. 2, 195–198

Let C be a boundedly weakly compact convex subset of a Banach space E. Suppose that each weakly compact convex subset of C possesses the fixed point property for nonexpansive mappings, and let T : C C be nonexpansive. In this note it is shown (by a very simple argument) that if a sequence of iterates of T (generated with the aid of an infinite, lower triangular, regular row-stochastic matrix) is bounded, then T has a fixed point.

Mathematical Subject Classification 2000
Primary: 47H10
Received: 14 April 1975
Published: 1 October 1975
Simeon Reich