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Abstract and Applied Analysis
Volume 2018, Article ID 3905632, 6 pages
https://doi.org/10.1155/2018/3905632
Research Article

Stability for Linear Volterra Difference Equations in Banach Spaces

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

Correspondence should be addressed to Rigoberto Medina; lc.sogalu@anidemr

Received 27 October 2017; Revised 23 December 2017; Accepted 16 January 2018; Published 1 March 2018

Academic Editor: Changbum Chun

Copyright © 2018 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

This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.