{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:30:16Z","timestamp":1760149816249,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,14]],"date-time":"2023-09-14T00:00:00Z","timestamp":1694649600000},"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 publication, we establish a suitable symmetry structure for orthogonal (\u03b1\u2212y\u2212G)-contractive mappings and prove fixed point results for an orthogonal (\u03b1\u2212y\u2212G)-contractive via orthogonal metric spaces. We give an application to strengthen our main results from the existing literature to prove the existence of a unique analytical solution to the differential equation by converting it into an integral equation through fixed point analysis.<\/jats:p>","DOI":"10.3390\/sym15091762","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T02:54:13Z","timestamp":1694746453000},"page":"1762","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fixed Point Results via Orthogonal (\u03b1\u2212y\u2212G)-Contraction in Orthogonal Complete Metric Space"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8904-6782","authenticated-orcid":false,"given":"Xiaolan","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China"},{"name":"Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong 643000, China"},{"name":"South Sichuan Center for Applied Mathematics, Zigong 643000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gunasekaran","family":"Nallaselli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Absar","family":"Haq","sequence":"additional","affiliation":[{"name":"Department of Natural Sciences and Humanities, University of Engineering and Technology (Narowal Campus), Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6346-605X","authenticated-orcid":false,"given":"Arul","family":"Gnanaprakasam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603203, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8941-2527","authenticated-orcid":false,"given":"Imran","family":"Baloch","sequence":"additional","affiliation":[{"name":"Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan"},{"name":"Higher Education Department, Government Graduate College for Boys Gulberg, Lahore 54600, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4064\/fm-3-1-133-181","article-title":"Sur les op\u00e9rations dans les ensembles abstraits et leur application aux \u00e9quations int\u00e9grales","volume":"3","author":"Banach","year":"1922","journal-title":"Fundam. 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