{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:01:56Z","timestamp":1760238116874,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,13]],"date-time":"2020-07-13T00:00:00Z","timestamp":1594598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Lucian Blaga University of Sibiu &amp; Hasso Plattner Foundation","award":["LBUS-IRG-2019-05"],"award-info":[{"award-number":["LBUS-IRG-2019-05"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Working in the setting of Banach spaces, we give a simpler proof of a result concerning the Ulam stability of the composition of operators. Several applications are provided. Then, we give an example of a discrete semigroup with Ulam unstable members and an example of Ulam stable operators on a Banach space, such that their sum is not Ulam stable. Another example is concerned with a     C 0    -semigroup      (  T t  )   t \u2265 0      of operators for which each     T t     is Ulam stable. We present an open problem concerning the Ulam stability of the members of the Bernstein     C 0    -semigroup. Two other possible problems are mentioned at the end of the paper.<\/jats:p>","DOI":"10.3390\/sym12071159","type":"journal-article","created":{"date-parts":[[2020,7,22]],"date-time":"2020-07-22T05:10:30Z","timestamp":1595394630000},"page":"1159","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Ulam Stability for the Composition of Operators"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1192-2281","authenticated-orcid":false,"given":"Ana Maria","family":"Acu","sequence":"first","affiliation":[{"name":"Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012 Sibiu, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5206-030X","authenticated-orcid":false,"given":"Ioan","family":"Ra\u015fa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Str. Memorandumului, No. 28, 400114 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,13]]},"reference":[{"key":"ref_1","unstructured":"Brzdek, J., Popa, D., Ra\u015fa, I., and Xu, B. (2018). Ulam stability of operators. Mathematical Analysis and Its Applications, Academic Press. [1st ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"107","DOI":"10.4134\/BKMS.2006.43.1.107","article-title":"Hyers-Ulam stability of a closed operator in a Hilbert space","volume":"43","author":"Hirasawa","year":"2006","journal-title":"Bull. Korean. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Brezis, H. (2010). 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Markov Operators, Positive Semigroups and Approximation Processes, 61, Walter de Gruyter. De Gruyter Studies in Mathematics.","DOI":"10.1515\/9783110366976"},{"key":"ref_16","first-page":"96","article-title":"Smoothness and shape preserving properties of Bernstein semigroup, Mediterr","volume":"15","year":"2018","journal-title":"J. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/7\/1159\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:50:44Z","timestamp":1760176244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/7\/1159"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,13]]},"references-count":16,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2020,7]]}},"alternative-id":["sym12071159"],"URL":"https:\/\/doi.org\/10.3390\/sym12071159","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,7,13]]}}}