具扰动的极大单调算子非线性随机方程(英文)

Nonlinear Random Equations of Maximal Monotone Operators with Perturbations

本文证明极大单调算子与一个单调算子的和是广义伪单调的;利用此结果与多值映射的可测选择理论,得出具扰动的极大单调算子非线性随机方程的解,把Browder[2,§7]的几个主要结果推广到随机情形。

In this paper, we prove that the sum T+S of two monotone operators T and S with T maximal mono-tone is generalized pseudo-monotone, and prove the existence of solutions of nonlinear random equations of maximal monotone operators with perturbations. Stochastic generalizations of main results in Browder [2, section 7] are obtained.