{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:42:48Z","timestamp":1760060568503,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T00:00:00Z","timestamp":1756857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12061050"],"award-info":[{"award-number":["12061050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The purpose of this paper is to establish the Oettli\u2013The\u00b4ra theorem in the setting of KM-type fuzzy b-metric spaces. To achieve this, we first prove a lemma that removes the constraints on the space coefficients, which significantly simplifies the proof process. Based on the Oettli\u2013The\u00b4ra theorem, we further demonstrate the equivalence of Ekeland variational principle, Caristi\u2019s fixed point theorem, and Takahashi\u2019s nonconvex minimization theorem in fuzzy b-metric spaces. Notably, the results obtained in this paper are consistent with the conditions of the corresponding theorems in classical fuzzy metric spaces, thereby extending the existing theories to the broader framework of fuzzy b-metric spaces.<\/jats:p>","DOI":"10.3390\/axioms14090679","type":"journal-article","created":{"date-parts":[[2025,9,3]],"date-time":"2025-09-03T15:15:57Z","timestamp":1756912557000},"page":"679","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Oettli-Th\u00e9ra Theorem and Ekeland Variational Principle in Fuzzy b-Metric Spaces"],"prefix":"10.3390","volume":"14","author":[{"given":"Xuan","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5638-0004","authenticated-orcid":false,"given":"Fei","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Lu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1017\/S0004972700015847","article-title":"Equivalents of Ekeland\u2019s principle","volume":"48","author":"Oettli","year":"1993","journal-title":"Bull. 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