{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:13:08Z","timestamp":1760145188844,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,6,25]],"date-time":"2024-06-25T00:00:00Z","timestamp":1719273600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deputyship for Research &amp; Innovation, Ministry of Education in Saudi Arabia","award":["ISP-2024"],"award-info":[{"award-number":["ISP-2024"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Our paper proposes a system of nonlinear mixed variational inequality problems (SNMVIPs) on Banach spaces. Under suitable assumptions, using the K-Fan fixed point theorem and Minty techniques, we demonstrate that the solution set to the SNMVIP is nonempty, weakly compact, and unique. Additionally, we suggest a stability result for the SNMVIPs by perturbing the duality mappings. Furthermore, we present an optimal control problem that is governed by the SNMVIPs and show that it can be solved.<\/jats:p>","DOI":"10.3390\/sym16070796","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T13:26:43Z","timestamp":1719494803000},"page":"796","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Solutions for the Nonlinear Mixed Variational Inequality Problem in the System"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7869-7731","authenticated-orcid":false,"given":"Husain","family":"Gissy","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}]},{"given":"Abdullah Ali H.","family":"Ahmadini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0496-3379","authenticated-orcid":false,"family":"Salahuddin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10898-006-9081-5","article-title":"Systems of generalized quasi-variational inclusions problems with applications with applications to variational analysis and optimization problems","volume":"38","author":"Lin","year":"2007","journal-title":"J. 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