SOME RANDOM FIXED POINT THEOREMS FOR RANDOM ASYMPTOTICALLY REGULAR OPERATORS

Poom Kumam, Somyot Plubtieng
2009 Demonstratio Mathematica  
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
more » ... of Domínguez [Fixed point theorems for uniformly Lipschitziane mappings and asymptotically regular mappings, Nonlinear Anal. 32 No. 1 (1998), 15-27]. 2000 Mathematics Subject Classification: 47H10, 47H09, 47H04.
doi:10.1515/dema-2009-0113 fatcat:5ucxkt22vfgxtj45xkdnqyedzu