{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T15:29:05Z","timestamp":1772292545193,"version":"3.50.1"},"reference-count":52,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,10,25]],"date-time":"2011-10-25T00:00:00Z","timestamp":1319500800000},"content-version":"vor","delay-in-days":297,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form \u0394[<jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic>) + <jats:italic>c<\/jats:italic><jats:italic>x<\/jats:italic>(<jats:italic>\u03c4<\/jats:italic>(<jats:italic>n<\/jats:italic>))] + <jats:italic>p<\/jats:italic>(<jats:italic>n<\/jats:italic>)<jats:italic>x<\/jats:italic>(<jats:italic>\u03c3<\/jats:italic>(<jats:italic>n<\/jats:italic>)) = 0, where <jats:italic>\u03c4<\/jats:italic>(<jats:italic>n<\/jats:italic>) is a general retarded argument, <jats:italic>\u03c3<\/jats:italic>(<jats:italic>n<\/jats:italic>) is a general deviated argument (retarded or advanced), <jats:italic>c<\/jats:italic> \u2208 <jats:italic>\u211d<\/jats:italic>, (<jats:italic>p<\/jats:italic>(<jats:italic>n<\/jats:italic>))\u2009<jats:sub><jats:italic>n<\/jats:italic>\u22650<\/jats:sub> is a sequence of positive real numbers such that <jats:italic>p<\/jats:italic>(<jats:italic>n<\/jats:italic>) \u2265 <jats:italic>p<\/jats:italic>, <jats:italic>p<\/jats:italic> \u2208 <jats:italic>\u211d<\/jats:italic><jats:sub>+<\/jats:sub>, and \u0394 denotes the forward difference operator \u0394<jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic>) = <jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic> + 1) \u2212 <jats:italic>x<\/jats:italic>(<jats:italic>n<\/jats:italic>). Also, we examine the asymptotic behavior of the solutions in case they are\ncontinuous and differentiable with respect to <jats:italic>c<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/2011\/262316","type":"journal-article","created":{"date-parts":[[2011,10,27]],"date-time":"2011-10-27T13:39:51Z","timestamp":1319722791000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Convergence and Divergence of the Solutions of a Neutral Difference Equation"],"prefix":"10.1155","volume":"2011","author":[{"given":"G. E.","family":"Chatzarakis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G. 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