Journal of the
Korean Mathematical Society JKMS

Some random fixed point theorems for nonexpansive and $*$-nonexpansive random operators defined on convex and starshaped sets in a Fr\'echet space are proved. Our work extends recent results of Beg and Shahzad and Tan and Yaun to noncontinuous multivalued random operators, sets analogue to an earlier result of Itoh and provides a random version of a deterministic fixed point theorem due to Singh and Chen.

Keywords: random fixed point, nonexpansive random operator, $*$-nonexpansive random operator, Chebyshev set, demiclosed map, Fr\'echet space

MSC numbers: 47H10, 54H25, 60H25