Geodesic
On the Uniform Convergence of Solutions of Volterra-Type Controlled Systems of Integral Equations Linear in the Control
Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 333-342

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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, weak convergence, Lipschitz operator, modulus of continuity.
Mots-clés : uniform convergence 
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     author = {Yu. I. Beloglazov and A. V. Dmitruk},
     title = {On the {Uniform} {Convergence} of {Solutions} of {Volterra-Type} {Controlled} {Systems} of {Integral} {Equations} {Linear} in the {Control}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {333--342},
     publisher = {mathdoc},
     volume = {96},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a2/}
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Yu. I. Beloglazov; A. V. Dmitruk. On the Uniform Convergence of Solutions of Volterra-Type Controlled Systems of Integral Equations Linear in the Control. Matematičeskie zametki, Tome 96 (2014) no. 3, pp. 333-342. http://geodesic.mathdoc.fr/item/MZM_2014_96_3_a2/