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

Hong Gang Li, Xian Bing Pan

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.

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ISSN: 1229-1595 (Print), 2466-0973 (Online)