Perturbations of maximal monotone random operators
Let X be a separable reflexive Banach space, \(X^*\) its topological dual and \(\Omega\) a measurable space. In this paper we present some new existence theorems for nonlinear random equations involving operators of monotone type. In Section 3 we study a nonlinear random equation of the form \[ (*)\quad y\in L(\omega)x+T(\omega)x \] where \(L: \Omega\times X\to 2^{X^*}\) is a multivalued maximal monotone random operator and \(T: \Omega\times X\to X^*\) a pseudomonotone bounded coercive random operator. In Section 4, we study a random equation of the form (*), when \(X=H\) is a Hilbert space, \(L: \Omega\times H\to H\) a linear maximal monotone random operator and \(T: \Omega\times H\to H\) a random operator that is of type (M), bounded and coercive. The approach that we follow is a combination of the existing deterministic theory, with techniques from the theory of measurable multifunctions.
existence theorems for nonlinear random equations involving operators of monotone type
multivalued maximal monotone random operator
scientific article; zbMATH DE number 3992570
scientific article