{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:25:37Z","timestamp":1760235937308,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T00:00:00Z","timestamp":1633392000000},"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>The main purpose of this paper is threefold. One is to study the existence and convergence problem of solutions for a class of generalized mixed quasi-variational hemivariational inequalities. The second one is to study the existence of optimal control for such kind of generalized mixed quasi-variational hemivariational inequalities under given control u\u2208U. The third one is to study the relationship between the optimal control and the data for the underlying generalized mixed quasi-variational inequality problems and a class of minimization problem. As an application, we utilize our results to study the elastic frictional problem in a class of Hilbert spaces. The results presented in the paper extend and improve upon some recent results.<\/jats:p>","DOI":"10.3390\/sym13101882","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Existence and Convergence Results for Generalized Mixed Quasi-Variational Hemivariational Inequality Problem"],"prefix":"10.3390","volume":"13","author":[{"given":"Shih-Sen","family":"Chang","sequence":"first","affiliation":[{"name":"Center for General Education, China Medical University, Taichung 40402, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0496-3379","authenticated-orcid":false,"family":"Salahuddin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jazan University, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunhe","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,5]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Error bounds for mixed set valued vector inverse quasi-variational inequalities","volume":"160","author":"Chang","year":"2020","journal-title":"J. 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