Vol. 38, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 306: 1
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
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