{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:12:05Z","timestamp":1760058725100,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T00:00:00Z","timestamp":1745193600000},"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>Starting from some systems of vector equilibrium problems, we obtain the existence of the solution for a class of weighted equilibrium problems, under different types of generalized pseudo-monotonicity assumptions. We present both new and previous results, making a connection between them and giving a few examples. Using the main theorem, we derive the solution existence for the initial systems and discuss a corresponding set-valued problem. Finally, we consider the case of a real normed space. We extend some previously obtained results from the literature about weighted variational inequalities, and we also give proofs for some results we previously announced. We give some relevant examples for our notions.<\/jats:p>","DOI":"10.3390\/axioms14040316","type":"journal-article","created":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T03:34:36Z","timestamp":1745206476000},"page":"316","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence Results for Some Classes of Weighted Equilibrium Problems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9947-7594","authenticated-orcid":false,"given":"Miruna-Mihaela","family":"Beldiman","sequence":"first","affiliation":[{"name":"\u201cG.Mihoc-C.Iacob\u201d Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Strada 13 Septembrie Nr. 13, 050711 Bucharest, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-5481-8021","authenticated-orcid":false,"given":"Andrei-Dan","family":"Halanay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bucharest University, Str. Academiei 14, 030018 Bucharest, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/s11117-019-00685-1","article-title":"New optimality conditions and a scalarization approach for a non-convex semi-vectorial bilevel optimization problem","volume":"24","author":"Lafhim","year":"2020","journal-title":"Positivity"},{"key":"ref_2","unstructured":"Younes, E., and Lafhim, L. (2024). Optimized problems with nonconvex multiobjective generalized Nash equilibrium problem constraints. Commun. Comb. Optim."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1007\/s00199-016-1031-y","article-title":"General economic equilibrium with financial markets and retainability","volume":"63","author":"Jofre","year":"2017","journal-title":"Econ. Theory"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Costea, N., Kristaly, A., and Varga, C. (2021). 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