{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:15:27Z","timestamp":1760242527225,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2017,9,16]],"date-time":"2017-09-16T00:00:00Z","timestamp":1505520000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The solvability of the following three-dimensional product-type system of difference equations              x  n + 1   = \u03b1  y n a   z  n \u2212 1  b  ,   y  n + 1   = \u03b2  z n c   x  n \u2212 1  d  ,   z  n + 1   = \u03b3  x n f   y  n \u2212 1  g  ,  n \u2208  N 0  ,     where     a , b , c , d , f , g \u2208 Z    ,     \u03b1 , \u03b2 , \u03b3 \u2208 C   \\   { 0 }     and      x  \u2212 i   ,  y  \u2212 i   ,  z  \u2212 i   \u2208 C   \\    { 0 }  ,         i \u2208 { 0 , 1 }    , is shown. This is the first three-dimensional system of the type with multipliers for which formulas are presented for their solutions in closed form in all the cases.<\/jats:p>","DOI":"10.3390\/sym9090195","type":"journal-article","created":{"date-parts":[[2017,9,19]],"date-time":"2017-09-19T07:12:50Z","timestamp":1505805170000},"page":"195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Solvable Three-Dimensional Product-Type System of Difference Equations with Multipliers"],"prefix":"10.3390","volume":"9","author":[{"given":"Stevo","family":"Stevi\u0107","sequence":"first","affiliation":[{"name":"Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36\/III, 11000 Beograd, Serbia"},{"name":"Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,9,16]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"On the rational recursive sequence xn+1 = axn\u22121\/(b + cxnxn\u22121)","volume":"43","author":"Migda","year":"2009","journal-title":"Tatra Mt. Math. Publ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1080\/10236190410001726421","article-title":"On impulsive Beverton-Holt difference equations and their applications","volume":"10","author":"Berezansky","year":"2004","journal-title":"J. Differ. Equ. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1016\/j.amc.2011.06.050","article-title":"On some systems of difference equations","volume":"218","author":"Berg","year":"2011","journal-title":"Appl. Math. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Iri\u010danin, B. (2010). 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