{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T11:41:55Z","timestamp":1780659715603,"version":"3.54.1"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"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 article, we modify the symmetry of orthogonal metric spaces and we prove common fixed point theorems via simulation functions in orthogonal Rectangular metric spaces. We also provide an illustrative example to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with a numerical simulation.<\/jats:p>","DOI":"10.3390\/sym14112420","type":"journal-article","created":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T02:31:27Z","timestamp":1668565887000},"page":"2420","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Common Fixed Point Theorems on Orthogonal Branciari Metric Spaces with an Application"],"prefix":"10.3390","volume":"14","author":[{"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":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2797-262X","authenticated-orcid":false,"given":"Senthil Kumar","family":"Prakasam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arul Joseph","family":"Gnanaprakasam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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, Al-Kharj 11942, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"given":"Khizar Hyatt","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stojan","family":"Radenovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF03018603","article-title":"Sur quelques points du calcul fonctionnel","volume":"22","author":"Frechet","year":"1906","journal-title":"Rend. 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