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

作者：Lan Heng you^*

来源：Computers & Mathematics with Applications, 2009, 57(4): 624-632.

DOI：10.1016/j.camwa.2008.09.036

• Non-monotone random set-valued operator
• Nonlinear random (A, eta)-resolvent operator equation with random relaxed cocoercive operator
• Random resolvent operator technique
• New generalized random iterative algorithm
• Existence and convergence

In this paper, we introduce and study a new class of nonlinear random (A, eta)-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, eta)-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, eta)-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.

• 出版日期2009-2
• 单位四川轻化工大学