{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T20:10:32Z","timestamp":1773519032982,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T00:00:00Z","timestamp":1695772800000},"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 manuscript, we establish some fixed-point theorems without continuity by using the triangular property on a fuzzy bipolar b-metric space as a generalized version and expansion of the well-known results. We also provide some examples and applications of the integral equation to the solution for our main results.<\/jats:p>","DOI":"10.3390\/sym15101831","type":"journal-article","created":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T07:38:46Z","timestamp":1695800326000},"page":"1831","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Fixed-Point Theorems on Fuzzy Bipolar b-Metric Spaces"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0449-5288","authenticated-orcid":false,"given":"Balaji","family":"Ramalingam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Panimalar Engineering College, Chennai 600123, Tamilnadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3877-2714","authenticated-orcid":false,"given":"Ozgur","family":"Ege","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Ege University, Izmir 35100, Turkey"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9578-2073","authenticated-orcid":false,"given":"Ahmad","family":"Aloqaily","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney 2150, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7986-886X","authenticated-orcid":false,"given":"Nabil","family":"Mlaiki","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"313","DOI":"10.2140\/pjm.1960.10.313","article-title":"Statistical metric spaces","volume":"10","author":"Schweizer","year":"1960","journal-title":"Pac. 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