Vol. 68, No. 1, 1977

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A random fixed point theorem for a multivalued contraction mapping

Shigeru Itoh

Vol. 68 (1977), No. 1, 85–90
Abstract

Some results on measurability of multivalued mappings are given. Then using them, the following random fixed point theorem is proved; Theorem. Let X be a Polish space, (T,𝒜) a measurable space. Let F : T × X CB(X) be a mapping such that for each x X, F(,x) is measurable and for each t T, F(t,) is k(t)-contraction, where k : T [0,1) is measurable. Then there exists a measurable mapping u : T X such that for every t T, u(t) F(t,u(t)).

Mathematical Subject Classification 2000
Primary: 54H25
Milestones
Received: 14 July 1976
Published: 1 January 1977
Authors
Shigeru Itoh