{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T20:10:30Z","timestamp":1773519030425,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T00:00:00Z","timestamp":1737676800000},"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 present the concept of (\u03a5,\u03a9)-iterativemappings in the setting of fuzzy bipolar metric space. The symmetric property in fuzzy bipolar metric spaces guarantees that the distance between any two elements remains invariant under permutation, ensuring consistency and uniformity in measurement regardless of the order in which the elements are considered. Furthermore, we prove several best proximity point results by utilizing (\u03a5,\u03a9)-fuzzy bipolar proximal contraction, (\u03a5,\u03a9)-Reich\u2013Rus\u2013Ciric type proximal contraction, (\u03a5,\u03a9)-Kannan type proximal contraction and (\u03a5,\u03a9)-Hardy\u2013Rogers type contraction. Furthermore, we provide some non-trivial examples to show the comparison with the existing results in the literature. At the end, we present an application to find the existence and uniqueness of a solution of an integral equation by applying the main result.<\/jats:p>","DOI":"10.3390\/sym17020180","type":"journal-article","created":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T10:46:07Z","timestamp":1737715567000},"page":"180","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Existence and Uniqueness Results for Fuzzy Bipolar Metric Spaces"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5228-1073","authenticated-orcid":false,"given":"Umar","family":"Ishtiaq","sequence":"first","affiliation":[{"name":"Office of Research, Innovation and Commercialization, University of Management and Technology, Lahore 54770, Pakistan"}]},{"given":"Fahad","family":"Jahangeer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University Islamabad, Islamabad 44000, Pakistan"}]},{"given":"Mubariz","family":"Garayev","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8042-1806","authenticated-orcid":false,"given":"Ioan-Lucian","family":"Popa","sequence":"additional","affiliation":[{"name":"Department of Computing, Mathematics and Electronics, \u201c1 Decembrie 1918\u201d University of Alba Iulia, 510009 Alba Iulia, Romania"},{"name":"Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,24]]},"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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