Vol. 38, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
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 theorems for nonlinear nonexpansive and generalized contraction mappings

William A. Kirk

Vol. 38 (1971), No. 1, 89–94
Abstract

Let X be a reflexive Banach space, H a closed convex subset of X, and let K be a nonempty, bounded, closed and convex subset of H which possesses normal structure. If T : K H is nonexpansive and if T : BK K where EK denotes the boundary of K relative to H, then T has a fixed point in K. This result generalizes an earlier theorem of the author, and a more recent theorem of F. E. Browder. An analogue is given for generalized contraction mappings in conjugate spaces.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 20 March 1970
Revised: 2 September 1970
Published: 1 July 1971
Authors
William A. Kirk