Random fixed points and random differential inclusions. (English) Zbl 0658.60090

Papageorgiou, Nikolaos S.

Int. J. Math. Math. Sci. 11, No. 3, 551-559 (1988).

Using the fixed point method the author studies random best approximations to random sets. The stochastic analogues of deterministic results of F. Browder and W. Petryshyn [J. Math. Anal. Appl. 20, 197-228 (1967; Zbl 0153.457)], K. Fan [Math. Z. 112, 234-240 (1969; Zbl 0185.395)] and S. Reich [J. Math. Anal. Appl. 62, 104- 113 (1978; Zbl 0375.47031)] are obtained. Two fixed point theorems for random multifunctions with stochastic domain are proved and some existence results for random differential inclusions are given.

Reviewer: O.Hadžić

MSC:

60H25	Random operators and equations (aspects of stochastic analysis)
47H10	Fixed-point theorems
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)

Keywords:

random fixed point theorem; fixed point theorems for random multifunctions; random differential inclusions

Citations:

Zbl 0153.457; Zbl 0185.395; Zbl 0375.47031