{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:41:03Z","timestamp":1760229663282,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,21]],"date-time":"2022-06-21T00:00:00Z","timestamp":1655769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001321","name":"National Research Foundation (NRF) of South Africa","doi-asserted-by":"publisher","award":["132108"],"award-info":[{"award-number":["132108"]}],"id":[{"id":"10.13039\/501100001321","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We perform a Lie analysis of (2k+2)th-order difference equations and obtain k+1 non-trivial symmetries. We utilize these symmetries to obtain their exact solutions. Sufficient conditions for convergence of solutions are provided for some specific cases. We exemplify our theoretical analysis with some numerical examples. The results in this paper extend to some work in the recent literature.<\/jats:p>","DOI":"10.3390\/sym14071290","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T23:11:19Z","timestamp":1655939479000},"page":"1290","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Symmetries, Reductions and Exact Solutions of a Class of (2k + 2)th-Order Difference Equations with Variable Coefficients"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3046-0679","authenticated-orcid":false,"given":"Mensah","family":"Folly-Gbetoula","sequence":"first","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Johannesburg 2000, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,21]]},"reference":[{"key":"ref_1","first-page":"21","article-title":"On the positive solutions of the difference equation xn+1 = xn\u22121\/(1 + xnxn\u22121)","volume":"150","author":"Cinar","year":"2004","journal-title":"Appl. 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