Nonlinear random operator equations and inequalities in Banach spaces

Antonios Karamolegos,Dimitrios Kravvaritis

doi:10.1155/s0161171292000139

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.

Highlights

In recent years the theory of random nonlinear operator equations has attracted the attention of many authors (e.g. Engl [1], Itoh [2,3], Kravvaritis [4,5], Papageorgiou [6])
We study perturbations of rdom mimM monotone operators by rdom operators of ty
We show that Le" 12 X X* is random

Summary

INTRODUCTION

In recent years the theory of random nonlinear operator equations has attracted the attention of many authors (e.g. Engl [1], Itoh [2,3], Kravvaritis [4,5], Papageorgiou [6]). We ben with a random fixed point threm which generMizes Threm 6 of cceri [9] In this d we fix (fl,,) to denote a complete, a-finite, meure spe. By [10, Theorem 6.1] fn is jointly meurable, so

Gr R

We set

We consider the multifunction