{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:16:56Z","timestamp":1760239016762,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,20]],"date-time":"2020-09-20T00:00:00Z","timestamp":1600560000000},"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>Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam\u2013Hyers stability result for the corresponding fixed point problem.<\/jats:p>","DOI":"10.3390\/sym12091554","type":"journal-article","created":{"date-parts":[[2020,9,20]],"date-time":"2020-09-20T21:20:28Z","timestamp":1600636828000},"page":"1554","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances"],"prefix":"10.3390","volume":"12","author":[{"given":"Veronica","family":"Ilea","sequence":"first","affiliation":[{"name":"Babe\u015f\u2013Bolyai University, Department of Mathematics, 1 M. Kog\u0103lniceanu Street, 400084 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5926-7760","authenticated-orcid":false,"given":"Diana","family":"Otrocol","sequence":"additional","affiliation":[{"name":"Technical University of Cluj-Napoca, Department of Mathematics, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania"},{"name":"Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,20]]},"reference":[{"unstructured":"Popov, E. (1966). Automatic Regulation and Control, (In Russian).","key":"ref_1"},{"doi-asserted-by":"crossref","unstructured":"Bainov, D.D., and Hristova, S. (2011). 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Jpn."},{"key":"ref_14","first-page":"125","article-title":"Fixed points, upper and lower fixed points: Abstract Gronwall lemmas","volume":"20","author":"Rus","year":"2004","journal-title":"Carpathian J. Math."},{"key":"ref_15","first-page":"305","article-title":"Remarks on Ulam stability of the operatorial equations","volume":"10","author":"Rus","year":"2009","journal-title":"Fixed Point Theory"},{"key":"ref_16","first-page":"405","article-title":"An application of the Picard operator technique to functional integral equations","volume":"18","author":"Ilea","year":"2017","journal-title":"J. Nonlinear Conv. Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1554\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:11:50Z","timestamp":1760177510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/9\/1554"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,20]]},"references-count":16,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2020,9]]}},"alternative-id":["sym12091554"],"URL":"https:\/\/doi.org\/10.3390\/sym12091554","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,9,20]]}}}