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Abstract and Applied Analysis
Volume 2016, Article ID 1319049, 6 pages
http://dx.doi.org/10.1155/2016/1319049
Research Article

Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces

Departamento de Ciencias Exactas, Universidad de Los Lagos, Casilla 933, Osorno, Chile

Received 25 June 2016; Accepted 30 October 2016

Academic Editor: Jozef Banas

Copyright © 2016 Rigoberto Medina. 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

We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.