{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:52:15Z","timestamp":1777449135382,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2014,8,1]],"date-time":"2014-08-01T00:00:00Z","timestamp":1406851200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p>\n                    Let X be an arbitrary Banach space. This work deals with the asymptotic behavior, the continuity and the compactness properties of solutions of the non-linear Volterra difference equation in X described by u(n+1)=\u03bb\u03a3\n                    <jats:sub>j=\u2212\u221e<\/jats:sub>\n                    <jats:sup>n<\/jats:sup>\n                    a(n\u2212j)u(j)+f(n,u(n)), n\u2208Z, for \u03bb in a distinguished subset of the complex plane, where a(n) is a complex summable sequence and the perturbation f is a non-Lipschitz nonlinearity. Concrete applications to control systems and integro-difference equations are given.\n                  <\/jats:p>","DOI":"10.3233\/asy-131213","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:33:20Z","timestamp":1575056000000},"page":"125-164","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Asymptotic analysis for Volterra difference equations"],"prefix":"10.1177","volume":"88","author":[{"given":"Claudio","family":"Cuevas","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidade Federal de Pernambuco, Recife-PE, CEP 50540-740, Brazil. E-mail: cch@dmat.ufpe.br"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario","family":"Choquehuanca","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica y Estad\u00edstica, Universidad de La Frontera, Casilla 54-D Temuco, Chile. E-mails: {mchoque@ufro.cl, herme.soto@ufrontera.cl}"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Herme","family":"Soto","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica y Estad\u00edstica, Universidad de La Frontera, Casilla 54-D Temuco, Chile. E-mails: {mchoque@ufro.cl, herme.soto@ufrontera.cl}"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2014,8,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131213","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-131213","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:08Z","timestamp":1777380008000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-131213"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.3233\/ASY-131213"],"URL":"https:\/\/doi.org\/10.3233\/asy-131213","relation":{"is-cited-by":[{"id-type":"doi","id":"10.1155\/2018\/6935069","asserted-by":"object"}]},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}