{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:24:20Z","timestamp":1760239460183,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2020,11,7]],"date-time":"2020-11-07T00:00:00Z","timestamp":1604707200000},"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-2020-06"],"award-info":[{"award-number":["LBUS-IRG-2020-06"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t\u22650 on C[0,1] such that for each t&gt;0, Rt is Ulam unstable. Moreover, we compute the central moments of Rt and establish a Voronovskaja-type formula. This enables to prove that C2[0,1] is contained in the domain D(A) of the infinitesimal generator of the semigroup. We raise the problem to fully characterize the domain D(A).<\/jats:p>","DOI":"10.3390\/sym12111844","type":"journal-article","created":{"date-parts":[[2020,11,8]],"date-time":"2020-11-08T20:23:35Z","timestamp":1604867015000},"page":"1844","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A C0-Semigroup of Ulam Unstable 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. 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 nr. 28, 400114 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2020,11,7]]},"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","unstructured":"Acu, A.M., and Ra\u015fa, I. (2020). Ulam Stability for the Composition of Operators. Symmetry, 12.","DOI":"10.3390\/sym12071159"},{"key":"ref_3","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_4","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.jmaa.2017.04.022","article-title":"Hyers-Ulam stability with respect to gauges","volume":"453","author":"Brzdek","year":"2017","journal-title":"J. Math. Anal. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1002\/mana.200310088","article-title":"Hyers-Ulam stability of linear differential operator with constant coefficients","volume":"258","author":"Miura","year":"2003","journal-title":"Math. Nachr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.exmath.2013.01.007","article-title":"On the stability of some classical operators from approximation theory","volume":"31","author":"Popa","year":"2013","journal-title":"Exp. Math."},{"key":"ref_7","first-page":"13","article-title":"On some classes of diffusion equations and related approximation problems","volume":"Volume 151","author":"Szabados","year":"2005","journal-title":"Trends and Applications in Constructive Approximation"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer.","DOI":"10.1007\/978-1-4612-5561-1"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/S1385-7258(70)80037-3","article-title":"On some linear positive operators","volume":"32","author":"Sikkema","year":"1970","journal-title":"Indag. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1844\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:30:29Z","timestamp":1760178629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/11\/1844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,7]]},"references-count":9,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["sym12111844"],"URL":"https:\/\/doi.org\/10.3390\/sym12111844","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,11,7]]}}}