{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:39:26Z","timestamp":1771677566113,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deputyship for Research &amp; Innovation, Ministry of Education in Saudi Arabia","award":["IF2\/PSAU\/2022\/01\/22334"],"award-info":[{"award-number":["IF2\/PSAU\/2022\/01\/22334"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this present study, we propose the concept of tricomplex-controlled metric spaces as a generalization of both controlled metric-type spaces and tricomplex metric-type spaces. In this work, we establish fixed point results using Banach, Kannan and Fisher-type contractions supported with nontrivial examples in the setting of the proposed space. We apply the derived result to find the analytical solution of an integral equation using the fixed point technique under the same metric.<\/jats:p>","DOI":"10.3390\/axioms12010056","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T03:27:44Z","timestamp":1672802864000},"page":"56","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Solving an Integral Equation via Tricomplex-Valued Controlled Metric Spaces"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9027-0810","authenticated-orcid":false,"given":"Rajagopalan","family":"Ramaswamy","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4191-3338","authenticated-orcid":false,"given":"Gunaseelan","family":"Mani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India"}],"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"}]},{"given":"Ola A. Ashour","family":"Abdelnaby","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"},{"name":"Department of Mathematics, Cairo University, Cairo 12613, Egypt"}],"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":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1007\/BF01443559","article-title":"Le Rappresentazioni Reali delle Forme Complesse a Gli Enti Iperalgebrici","volume":"40","author":"Segre","year":"1892","journal-title":"Math. 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