{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:06:06Z","timestamp":1760234766876,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T00:00:00Z","timestamp":1624320000000},"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>Symmetries play an important role in the dynamics of physical systems. As an example, quantum physics and microworld are the basis of symmetry principles. These problems are reduced to solving inequalities in general. That is why in this article, we study the numerical approximation of solutions to variational inequality problems involving quasimonotone operators in an infinite-dimensional real Hilbert space. We prove that the iterative sequences generated by the proposed iterative schemes for solving variational inequalities with quasimonotone mapping converge strongly to some solution. The main advantage of the proposed iterative schemes is that they use a monotone and non-monotone step size rule based on operator knowledge rather than a Lipschitz constant or some line search method. We present a number of numerical experiments for the proposed algorithms.<\/jats:p>","DOI":"10.3390\/sym13071108","type":"journal-article","created":{"date-parts":[[2021,6,22]],"date-time":"2021-06-22T22:10:59Z","timestamp":1624399859000},"page":"1108","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Class of Novel Mann-Type Subgradient Extragradient Algorithms for Solving Quasimonotone Variational Inequalities"],"prefix":"10.3390","volume":"13","author":[{"given":"Nopparat","family":"Wairojjana","sequence":"first","affiliation":[{"name":"Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), 1 Moo 20 Phaholyothin Road, Klong Neung, Klong Luang, Pathumthani 13180, Thailand"}]},{"given":"Ioannis\u00a0K.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1454-2962","authenticated-orcid":false,"given":"Meshal","family":"Shutaywi","sequence":"additional","affiliation":[{"name":"Department of Mathematics College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5022-2558","authenticated-orcid":false,"given":"Wejdan","family":"Deebani","sequence":"additional","affiliation":[{"name":"Department of Mathematics College of Science & Arts, King Abdulaziz University, P.O. Box 344, Rabigh 21911, Saudi Arabia"}]},{"given":"Christopher I.","family":"Argyros","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Oklahoma, Norman, OK 73071, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,22]]},"reference":[{"key":"ref_1","first-page":"4413","article-title":"Formes bilin\u00e9aires coercitives sur les ensembles convexes","volume":"258","author":"Stampacchia","year":"1964","journal-title":"C. R. Hebd. Seances Acad. Sci."},{"key":"ref_2","first-page":"77","article-title":"On systems of variational inequalities","volume":"41","author":"Konnov","year":"1997","journal-title":"Rus. Math. 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