Approximation solvability of nonlinear random (A,η)(A,η)-resolvent operator equations with random relaxed cocoercive operators

In this paper, we introduce and study a new class of nonlinear random (A,η)(A,η)-resolvent operator equations with random relaxed cocoercive operators in Hilbert spaces. By using Chang’s lemma, Theorem 3.1 of Liu and Li, and the resolvent operator technique for (A,η)(A,η)-monotone operators due to Lan, we also prove the existence theorems of the solutions and convergence theorems of the new generalized random iterative procedures with errors for this nonlinear random (A,η)(A,η)-resolvent operator equations involving non-monotone random set-valued operators in Hilbert spaces. The results presented in this paper improve and generalize some known corresponding results in the literature.