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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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 672–682. https://doi.org/10.33048/smzh.2021.62.317
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Tolstonogov, A.A. A Multivalued History-Dependent Operator and Implicit Evolution Inclusions. I. Sib Math J 62, 545–553 (2021). https://doi.org/10.1134/S0037446621030174
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DOI: https://doi.org/10.1134/S0037446621030174