International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 551-559

Random fixed points and random differential inclusions

Nikolaos S. Papageorgiou

University of California, 1015 Department of Mathematics, Davis 95616, California, USA

Received 28 July 1987; Revised 19 October 1987

Copyright © 1988 Nikolaos S. Papageorgiou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, first, we study random best approximations to random sets, using fixed point techniques, obtaining this way stochastic analogues of earlier deterministic results by Browder-Petryshyn, KyFan and Reich. Then we prove two fixed point theorems for random multifunctions with stochastic domain that satisfy certain tangential conditions. Finally we consider a random differential inclusion with upper semicontinuous orientor field and establish the existence of random solutions.