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A Multivalued History-Dependent Operator and Implicit Evolution Inclusions. I

Authors
  • Tolstonogov, A. A.1
  • 1 Matrosov Institute of Systems Dynamics and Control, Irkutsk, Russia , Irkutsk (Russia)
Type
Published Article
Journal
Siberian Mathematical Journal
Publisher
Pleiades Publishing
Publication Date
May 27, 2021
Volume
62
Issue
3
Pages
545–553
Identifiers
DOI: 10.1134/S0037446621030174
Source
Springer Nature
Keywords
License
Yellow

Abstract

On the space of continuous functions from a line segment to a reflexive Banach space, we consider some operator whose values are closed convex subsets of the space. If the values are singletons, the operator becomes a well-known single-valued history-dependent operator. We study the properties of the operator, prove a fixed-point theorem analogous to the fixed-point theorem for single-valued history-dependent operators, and provide some examples. The results are applied to study implicit (unresolved for derivatives) evolution inclusions with maximal monotone operators and with perturbations in a Hilbert space. These perturbations are single-valued and multivalued history-dependent operators.

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