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The purpose of this paper is to prove some random fixed point theorem for multivalued nonexpansive non-self random operators. We will prove the existence of a random fixed point theorem for multivalued non-self random operator in the framework of a Banach space with property (D), and satisfying an inwardness condition. Our work also extends the stochastic version of the results of Kumam [P. Kumam, A note on some fixed point theorems for set-valued non-self mappings in Banach spaces. Int. Journal of Math. Analysis, to appear.], and improves the work of Kumam and Plubtieng [P. Kumam and S. Plubtieng, Random fixed point theorems for multivalued nonexpansive operators in uniformly nonsquare Banach spaces.  Random Oper. and Stoch. Equ . 14(1) (2006), 35–44.].

Random fixed points of multivalued random operators with property (D)