Nonlinear random operator equations and inequalities in Banach spaces

Abstract

In this paper we give some new existence theorems for nonlinear random equations and inequalities involving operators of monotone type in Banach spaces. A random Hammerstein integral equation is also studied. In order to obtain random solutions we use some results from the existing deterministic theory as well as from the theory of measurable multifunctions and, in particular, the measurable selection theorems of Kuratowski/Ryll-Nardzewski and of Saint-Beuve.

Keywords

• random equations and inequalities
• operators of monotone type
• coercive operators
• measurable multifunctions.