On the Uniform Convergence of Solutions of Volterra-Type Controlled Systems of Integral Equations Linear in the Control

Yu. I. Beloglazov, A. V. Dmitruk

M. V. Lomonosov Moscow State University

Abstract: For systems of integral equations with properties cited in the title, we propose a constraint on the convergence of the controls guaranteeing the uniform convergence of the solutions of such systems. This requirement is weaker than weak convergence. Relevant examples are given.

Keywords: Volterra-type controlled system, uniform convergence, weak convergence, Lipschitz operator, modulus of continuity.

UDC: 517.968.22

Received: 21.09.2013

DOI: 10.4213/mzm10515

 English version: Mathematical Notes, 2014, 96:3, 317–325

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