Vol. 44, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
A bifurcation theorem for k-set contractions

James William Thomas

Vol. 44 (1973), No. 2, 749–756
Abstract

One of the the most often used results of bifurcation theory is the following theorem. Let C be a compact mapping from the Banach space X into itself. Suppose that C is such that C(𝜃) = 𝜃 and the derivative of C exists at x = 𝜃. Then each characteristic value, μ0, of odd multiplicity of C(𝜃) is a bifurcation point of C, and to this bifurcation point there corresponds a continuous branch of eigenvectors of C. The main result in this paper will show that the above theorem can be extended to a class of non-compact mapping of the form I f where f is a k-set contraction.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 29 October 1971
Published: 1 February 1973
Authors
James William Thomas