APPROXIMATION SOLUTION FOR NONLINEAR SET-VALUED MIXED RANDOM VARIATIONAL INCLUSIONS INVOLVING RANDOM NONLINEAR (A_{\omega}, \eta_{\omega})-MONOTONE MAPPINGS

Abstract

In this paper, we introduce and study a new class of nonlinear set-valued mixed random variational inclusions involving random nonlinear (A_{\omega}, \eta_{\omega})-monotone Mappings in Hilbert spaces. Based on the generalized random resolvent operator associated with random nonlinear (A_{\omega}, \eta_{\omega})-monotone mappings, an existence theorem of solutions for this kind of random nonlinear set-valued mixed variational inclusions is established and a new algorithm of approximation solution is suggested and discussed. The results presented in this paper generalize, improve, and unify some recent results in this field.