Perturbations of maximal monotone random operators
type: Item
instance of: scholarly article
title: Perturbations of maximal monotone random operators
zbMATH Open document ID: 0613.60061
DOI: 10.1016/0024-3795(86)90322-8
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 47H05
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 3992570
zbMATH Keywords: operators of type (M)
zbMATH Keywords: coercivity
zbMATH Keywords: existence theorems for nonlinear random equations involving operators of monotone type
zbMATH Keywords: multivalued maximal monotone random operator
author: Dimitrios Kravvaritis
author: Nikos M. Stavrakakis
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90322-8
OpenAlex ID: W1982702276
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description: scientific article; zbMATH DE number 3992570