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SOME RANDOM FIXED POINT THEOREMS FOR RANDOM ASYMPTOTICALLY REGULAR OPERATORS

2009
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Demonstratio Mathematica
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Let (Q, E) be a measurable space, X a Banach space, C a weakly compact convex subset of X and T : fi x C -> C a random operator. Let WCS(X) be the weakly convergent sequence coefficient of X and (X) its Lifschitz characteristic. If T is asymptotically regular and assume that there exists u> € Cl and constant c such that + ^1+4WCS(X)(K W (X)-1) <r(T( w, •)) <c< , we prove that T has a random fixed point. Our results also give stochastic version gener alization of some results of Domínguez [Fixed

doi:10.1515/dema-2009-0113
fatcat:5ucxkt22vfgxtj45xkdnqyedzu