{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:05:50Z","timestamp":1760058350653,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T00:00:00Z","timestamp":1742947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland\u2019s variational principle. As a consequence, we also derive a variant of Caristi\u2019s fixed-point theorem.<\/jats:p>","DOI":"10.3390\/axioms14040250","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T04:11:40Z","timestamp":1743135100000},"page":"250","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fixed-Point Results and the Ekeland Variational Principle in Vector B-Metric Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0153-6168","authenticated-orcid":false,"given":"Radu","family":"Precup","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science and Institute of Advanced Studies in Science and Technology, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"},{"name":"Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4903-4119","authenticated-orcid":false,"given":"Andrei","family":"Stan","sequence":"additional","affiliation":[{"name":"Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania"},{"name":"Department of Mathematics, Babe\u015f-Bolyai University, 400084 Cluj-Napoca, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"675","DOI":"10.2307\/2371174","article-title":"On Quasi-Metric Spaces","volume":"53","author":"Wilson","year":"1931","journal-title":"Am. J. Math."},{"key":"ref_2","first-page":"26","article-title":"The contraction mapping principle in quasimetric spaces","volume":"30","author":"Bakhtin","year":"1989","journal-title":"Funct. Anal. Unianowsk Gos. Ped. 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