{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T08:39:38Z","timestamp":1768725578449,"version":"3.49.0"},"reference-count":40,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T00:00:00Z","timestamp":1635811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we present sufficient conditions in order to establish different types of Ulam stabilities for a class of higher order integro-differential equations. In particular, we consider a new kind of stability, the \u03c3-semi-Hyers-Ulam stability, which is in some sense between the Hyers\u2013Ulam and the Hyers\u2013Ulam\u2013Rassias stabilities. These new sufficient conditions result from the application of the Banach Fixed Point Theorem, and by applying a specific generalization of the Bielecki metric.<\/jats:p>","DOI":"10.3390\/sym13112068","type":"journal-article","created":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T22:14:52Z","timestamp":1635891292000},"page":"2068","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4772-4300","authenticated-orcid":false,"given":"Alberto M.","family":"Sim\u00f5es","sequence":"first","affiliation":[{"name":"CMA-UBI, University of Beira-Interior, 6201-001 Covilh\u00e3, Portugal"},{"name":"The Center for Research & Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193 Aveiro, Portugal"},{"name":"Department of Mathematics, University of Beira Interior, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3164-113X","authenticated-orcid":false,"given":"Fernando","family":"Carapau","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es (CIMA), University of \u00c9vora, 7000-671 \u00c9vora, Portugal"},{"name":"Department of Mathematics, University of \u00c9vora, 7000-671 \u00c9vora, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7652-6119","authenticated-orcid":false,"given":"Paulo","family":"Correia","sequence":"additional","affiliation":[{"name":"Centro de Investiga\u00e7\u00e3o em Matem\u00e1tica e Aplica\u00e7\u00f5es (CIMA), University of \u00c9vora, 7000-671 \u00c9vora, Portugal"},{"name":"Department of Mathematics, University of \u00c9vora, 7000-671 \u00c9vora, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,2]]},"reference":[{"key":"ref_1","unstructured":"Ulam, S.M. 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