{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T01:32:35Z","timestamp":1781746355957,"version":"3.54.5"},"reference-count":36,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,15]],"date-time":"2023-12-15T00:00:00Z","timestamp":1702598400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","doi-asserted-by":"publisher","award":["IMSIU-RP23069"],"award-info":[{"award-number":["IMSIU-RP23069"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton\u2019s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric.<\/jats:p>","DOI":"10.3390\/sym15122205","type":"journal-article","created":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T05:41:35Z","timestamp":1702878095000},"page":"2205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2909-8753","authenticated-orcid":false,"given":"Cemil","family":"Tun\u00e7","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65090, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3110-414X","authenticated-orcid":false,"given":"Fehaid Salem","family":"Alshammari","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fahir Talay","family":"Akyildiz","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,15]]},"reference":[{"key":"ref_1","unstructured":"Burton, T.A. 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