A note on H-convergence

O.P. Kogut; P.I. Kogut; T.N. Rudyanova

doi:10.15421/240923

A note on H-convergence

O.P. Kogut (Institute of Applied System Analysis, National Technical University KPI)
P.I. Kogut (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0003-1593-0510
T.N. Rudyanova (Dnipropetrovsk State Finance Academy), https://orcid.org/0000-0002-8685-4132

Abstract

In this paper we study the H-convergence property for the uniformly bounded sequences of square matrices $$$\left\{ A_{\varepsilon} \in L^{\infty} (D; \mathbb{R}^{n \times n}) \right\}_{\varepsilon > 0}$$$. We derive the sufficient conditions, which guarantee the coincidence of $$$H$$$-limit with the weak-* limit of such sequences in $$$L^{\infty} (D; \mathbb{R}^{n \times n})$$$.

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