{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T22:24:02Z","timestamp":1773267842118,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,6]],"date-time":"2022-10-06T00:00:00Z","timestamp":1665014400000},"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 paper, we introduce the notion of neutrosophic rectangular triple-controlled metric space, relaxing the symmetry requirement of neutrosophic metric spaces, by replacing triangular inequalities with rectangular inequalities, and prove fixed point theorems. We have derived several interesting results for contraction mappings supplemented with non-trivial examples. The derived results have been applied to prove the existence of a unique analytical solution as well as a closed form of the unique solution to the integral equation.<\/jats:p>","DOI":"10.3390\/sym14102074","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T03:32:56Z","timestamp":1665459176000},"page":"2074","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solution of Integral Equation with Neutrosophic Rectangular Triple Controlled Metric Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4191-3338","authenticated-orcid":false,"given":"Gunaseelan","family":"Mani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9027-0810","authenticated-orcid":false,"given":"Rajagopalan","family":"Ramaswamy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, ALkharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arul Joseph","family":"Gnanaprakasam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chennai 603203, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1687-3212","authenticated-orcid":false,"given":"Ola A Ashour","family":"Abdelnaby","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India"},{"name":"Department of Mathematics, Cairo University, Cairo 12613, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1845-4441","authenticated-orcid":false,"given":"Slobodan","family":"Radojevic","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrad, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les operations dans les ensembles abstraits et leur application aux equations integrales","volume":"3","author":"Banach","year":"1922","journal-title":"Fund. 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