• Korean Journal of Mathematics
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• v.10 no.1
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• pp.19-23
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• 2002

Let X be a Banach space satisfying Opial's condition, C a weakly compact convex subset of $X,F:C{\rightarrow}X$ a nonexpansive map, and let $G:C{\rightarrow}X$ be a compact and demiclosed map. We prove that F + G has a fixed point in C if $F+G:C{\rightarrow}X$ is a weakly inward map.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.51-60
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• 2002

Some random fixed point theorems for nonexpansive and *-nonexpansive random operators defined on convex and star-shaped sets in a Frechet 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.