Generalized Nonlinear Variational Inequality Problems with Random Variation

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. By leveraging the Fan-KKM theorem and Aumann’s measurable selection theorem, we can establish the existence and uniqueness of random solution sets, given the conditions of monotonicity and convexity. Additionally, we use Minty’s lemma to demonstrate the compactness and convexity of the random solution sets.