{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T13:58:57Z","timestamp":1762783137001,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T00:00:00Z","timestamp":1721260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Jouf University","award":["DGSSR-2024-02-01049"],"award-info":[{"award-number":["DGSSR-2024-02-01049"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam\u2019s notion of stability is highly helpful since it provides a range of estimates between exact and approximate solutions. Using Brzd\u0229k\u2019s fixed point technique (FPT), we establish the stability of the following cubic type functional equations (CFUEQs): F\u03be13+\u03be233+F\u03be13\u2212\u03be233=2F(\u03be1)+2F(\u03be2),2F\u03be13+\u03be2323=F(\u03be1)+F(\u03be2) for all \u03be1,\u03be2\u2208R.<\/jats:p>","DOI":"10.3390\/axioms13070480","type":"journal-article","created":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T10:39:26Z","timestamp":1721299166000},"page":"480","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Stability Results for Some Classes of Cubic Functional Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4955-0842","authenticated-orcid":false,"given":"El-sayed","family":"El-hady","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8019-3655","authenticated-orcid":false,"given":"Yamin","family":"Sayyari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5348-1333","authenticated-orcid":false,"given":"Mehdi","family":"Dehghanian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sirjan University of Technology, Sirjan 7813733385, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6562-9705","authenticated-orcid":false,"given":"Ymnah","family":"Alruwaily","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,18]]},"reference":[{"unstructured":"Acz\u00e9l, J. (1966). Lectures on Functional Equations and Their Applications, Academic Press.","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Nassar, H., and El-Hady, E.S. (2016). Closed-form solution of a LAN gateway queueing model. Contributions in Mathematics and Engineering: In Honor of Constantin Carath\u00e9odory, Springer.","key":"ref_2","DOI":"10.1007\/978-3-319-31317-7_20"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1007\/s00010-016-0421-3","article-title":"A note on solutions of a functional equation arising in a queuing model for a LAN gateway","volume":"90","author":"Lesniak","year":"2016","journal-title":"Aequationes Math."},{"unstructured":"Ulam, S.M. (1960). 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