{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:43Z","timestamp":1753881223266,"version":"3.41.2"},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,3,27]],"date-time":"2012-03-27T00:00:00Z","timestamp":1332806400000},"content-version":"vor","delay-in-days":86,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10771050"],"award-info":[{"award-number":["10771050"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>We introduce and study a system of generalized nonlinear mixed variational\u2010like inequality problems (SGNMVLIPs) in Banach spaces. The auxiliary principle technique is applied to study the existence and iterative algorithm of solutions for the SGNMVLIP. First, the existence of solutions of the auxiliary problems for the SGNMVLIP is shown. Second, an iterative algorithm for solving the SGNMVLIP is constructed by using this existence result. Finally, not only the existence of solutions of the SGNMVLIP is shown but also the convergence of iterative sequences generated by the algorithm is also proven. The technique and results presented in this paper generalize and unify the corresponding techniques and results given in the literature.<\/jats:p>","DOI":"10.1155\/2012\/176283","type":"journal-article","created":{"date-parts":[[2012,3,27]],"date-time":"2012-03-27T21:33:33Z","timestamp":1332884013000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Existence and Iterative Algorithm of Solutions for a System of Generalized Nonlinear Mixed Variational\u2010Like Inequalities"],"prefix":"10.1155","volume":"2012","author":[{"given":"Yan-Mei","family":"Du","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,3,27]]},"reference":[{"key":"e_1_2_5_1_2","first-page":"4413","article-title":"Formes bilin\u00e9aires coercitives sur les ensembles convexes","volume":"258","author":"Stampacchia G.","year":"1964","journal-title":"Les Comptes Rendus de l\u2032Acad\u00e9mie des Sciences"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/817436"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-004-1182-z"},{"key":"e_1_2_5_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/768272"},{"key":"e_1_2_5_5_2","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1812-2011-101"},{"key":"e_1_2_5_6_2","first-page":"63","article-title":"Mixed variational-like inequalities","volume":"1","author":"Noor M. 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