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Discrete Dynamics in Nature and Society
Volume 7 (2002), Issue 1, Pages 19-22
http://dx.doi.org/10.1080/10260220290013471

Boundedness of solutions of matrix nonlinear volterra difference equations

1Department of Mathematics, Ben Gurion University of the Negev, PO. Box 653, Beer-Sheva 84105, Israel
2Departmento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile

Received 8 February 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Nonlinear discrete-time Volterra equations in a Euclidean space are considered. Conditions for the boundedness of solutions are established by virtue of recent estimates for the norm of the resolvent of Volterra operators. The conditions are formulated in the terms of coefficients of considered equations. In addition, estimates for the c0- and l2-norms of solutions are derived.