Random fixed-point theorems and approximation in cones. (English) Zbl 0856.47036

Tan, Kok-Keong; Yuan, Xian-Zhi

J. Math. Anal. Appl. 185, No. 2, 378-390 (1994); corrigendum ibid. 195, No. 2, 619 (1995).

A very general random fixed point theorem is first proved. As applications, some random approximation theorems and random fixed-point theorems are obtained. Recent results due to S. Itoh [J. Math. Anal. Appl. 67, 261-273 (1979; Zbl 0407.60069)], T.-C. Lin [Proc. Am. Math. Soc. 102, No. 3, 502-506 (1988; Zbl 0653.47033)], and H. Xu [Proc. Am. Math. Soc. 110, No. 2, 395-400 (1990; 716.47029)] either are improved or are direct consequences of our results. The stochastic versions of the recent results of G. Li [Proc. Am. Math. Soc. 97, 277-280 (1986; Zbl 0592.47046)] are also given.

Reviewer: J.Appell (Würzburg)

MSC:

47H10	Fixed-point theorems
47H40	Random nonlinear operators
60H25	Random operators and equations (aspects of stochastic analysis)

Keywords:

random fixed point theorem; random approximation theorems

Citations:

Zbl 0407.60069; Zbl 0653.47033; Zbl 0716.47029; Zbl 0592.47046