{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:08:11Z","timestamp":1778494091517,"version":"3.51.4"},"reference-count":82,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,2]],"date-time":"2022-07-02T00:00:00Z","timestamp":1656720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Jouf University","award":["DSR-2021-03-03158"],"award-info":[{"award-number":["DSR-2021-03-03158"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Ulam stability is motivated by the following issue: how much an approximate solution of an equation differs from the exact solutions to the equation. It is connected to some other areas of investigation, e.g., optimization, approximation theory and shadowing. In this paper, we present and discuss the published results on such stability for functional equations in the classes of function-taking values in 2-normed spaces. In particular, we point to several pitfalls they contain and provide possible simple improvements to some of them. Thus we show that the easily noticeable symmetry between them and the analogous results proven for normed spaces is, in fact, mainly apparent. Our article complements the earlier similar review published in Symmetry (13(11), 2200) because it concerns the outcomes that have not been discussed in this earlier publication.<\/jats:p>","DOI":"10.3390\/sym14071365","type":"journal-article","created":{"date-parts":[[2022,7,4]],"date-time":"2022-07-04T23:38:55Z","timestamp":1656977935000},"page":"1365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["On Ulam Stability of Functional Equations in 2-Normed Spaces\u2014A Survey II"],"prefix":"10.3390","volume":"14","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\/0000-0002-6529-4885","authenticated-orcid":false,"given":"Janusz","family":"Brzd\u0119k","sequence":"additional","affiliation":[{"name":"Faculty of Applied Mathematics, AGH University of Science and Technology, Mickiewicza 30, 30-059 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.apnum.2004.08.011","article-title":"A survey of shadowing methods for numerical solutions of ordinary differential equations","volume":"53","author":"Hayes","year":"2005","journal-title":"Appl. Numer. 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