{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:44:41Z","timestamp":1760229881988,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,29]],"date-time":"2022-06-29T00:00:00Z","timestamp":1656460800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"2020 Shanghai Leading Talents Program of the Shanghai Municipal Human Resources and Social Security Bureau","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]},{"name":"Innovation Program of Shanghai Municipal Education Commission","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]},{"name":"Program for Outstanding Academic Leaders in Shanghai City","award":["20LJ2006100","15ZZ068","15XD1503100"],"award-info":[{"award-number":["20LJ2006100","15ZZ068","15XD1503100"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In real Banach spaces, the concept of \u03b1-well-posedness is extended to the class of generalized hemivariational inequalities systems consisting of two parts which are of symmetric structure mutually. First, certain concepts of \u03b1-well-posedness for generalized hemivariational inequalities systems are put forward. Second, certain metric characterizations of \u03b1-well-posedness for generalized hemivariational inequalities systems are presented. Lastly, certain equivalence results between strong \u03b1-well-posedness of both the system of generalized hemivariational inequalities and its system of derived inclusion problems are established.<\/jats:p>","DOI":"10.3390\/sym14071341","type":"journal-article","created":{"date-parts":[[2022,6,30]],"date-time":"2022-06-30T01:38:48Z","timestamp":1656553128000},"page":"1341","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Characterizations of Well-Posedness for Generalized Hemivariational Inequalities Systems with Derived Inclusion Problems Systems in Banach Spaces"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3730-1475","authenticated-orcid":false,"given":"Lu-Chuan","family":"Ceng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Jian-Ye","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Cong-Shan","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Fang-Fei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Hui-Ying","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Yun-Ling","family":"Cui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Long","family":"He","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/0041-5553(66)90003-6","article-title":"On the stability of the functional optimization problem","volume":"6","author":"Tykhonov","year":"1966","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/s10957-008-9428-9","article-title":"Well-posedness for mixed quasivariational-like inequalities","volume":"139","author":"Ceng","year":"2008","journal-title":"J. Optim. Theory Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.2298\/FIL1407345C","article-title":"Levitin-Polyak well-posedness for set-valued optimization problems with constraints","volume":"28","author":"Chen","year":"2014","journal-title":"Filomat"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.camwa.2007.03.019","article-title":"Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints","volume":"55","author":"Fang","year":"2008","journal-title":"Comput. Math. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2435","DOI":"10.11650\/twjm\/1500406083","article-title":"Well-posedness of systems of equilibrium problems","volume":"14","author":"Hu","year":"2010","journal-title":"Taiwanese J. Math."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1137\/040614943","article-title":"Generalized Levitin-Polyak well-posedness in constrained optimization","volume":"17","author":"Huang","year":"2006","journal-title":"SIAM J. Optim."},{"key":"ref_7","first-page":"71","article-title":"Well-posedness, conditioning, and regularization of minimization, inclusion, and fixed-point problems","volume":"12","author":"Lemaire","year":"1998","journal-title":"Pliska Stud. Math. Bulgar."},{"key":"ref_8","first-page":"764","article-title":"Convergence of minimizing sequences in conditional extremum problems","volume":"7","author":"Levitin","year":"1966","journal-title":"Soviet Math. Dokl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s10957-005-7561-2","article-title":"Well-posedness and L-well-posedness for quasivariational inequalities","volume":"128","author":"Lignola","year":"2006","journal-title":"J. Optim. Theory Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"3609","DOI":"10.1016\/j.na.2008.07.018","article-title":"Well-posedness in the generalized sense for variational inclusion and disclusion problems and well-posedness for optimization problems with constraint","volume":"70","author":"Lin","year":"2009","journal-title":"Nonlinear Anal."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF02192292","article-title":"Extended well-posedness of optimization problems","volume":"91","author":"Zolezzi","year":"1996","journal-title":"J. Optim. Theory Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1080\/01630568108816100","article-title":"A characterization of Tykhonov well-posedness for minimum problems with applications to variational inequalities","volume":"3","author":"Lucchetti","year":"1981","journal-title":"Numer. Funct. Anal. Optim."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1080\/01630569508816652","article-title":"Well-posed hemivariational inequalities","volume":"16","author":"Goeleven","year":"1995","journal-title":"Numer. Funct. Anal. Optim."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.22436\/jnsa.009.03.44","article-title":"Equivalence of well-posedness between systems of hemivariational inequalities and inclusion problems","volume":"9","author":"Wang","year":"2016","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3879","DOI":"10.22436\/jnsa.009.06.35","article-title":"On the well-posedness of generalized hemivariational inequalities and inclusion problems in Banach spaces","volume":"9","author":"Ceng","year":"2016","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"264721","DOI":"10.1155\/2012\/264721","article-title":"Metric characterizations of \u03b1-well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces","volume":"2012","author":"Ceng","year":"2012","journal-title":"J. Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Carl, S., Le, V.K., and Motreanu, D. (2007). Nonsmooth Variational Problems and Their Inequalities: Comparison Principles and Applications, Springer.","DOI":"10.1007\/978-0-387-46252-3"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Clarke, F.H. (1990). Optimization and Nonsmooth Analysis, SIAM.","DOI":"10.1137\/1.9781611971309"},{"key":"ref_19","unstructured":"Kuratowski, K. (1968). Topology, Academic Press."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Migorski, S., Ochal, A., and Sofonea, M. (2013). Nonlinear Inclusions and Hemivariational Inequalities: Models and Analysis of Contact Problems, Springer.","DOI":"10.1007\/978-1-4614-4232-5"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zeidler, E. (1990). Nonlinear Functional Analysis and Its Applications, Springer.","DOI":"10.1007\/978-1-4612-0981-2"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1877","DOI":"10.1007\/s40840-021-01214-8","article-title":"Existence results for a class of variational quasi-mixed hemivariational-like inequalities","volume":"45","author":"Mahalik","year":"2022","journal-title":"Bull. Malays. Math. Sci. Soc."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Migorski, S., and Long, F.Z. (2020). Constrained variational-hemivariational inequalities on nonconvex star-shaped sets. Mathematics, 8.","DOI":"10.3390\/math8101824"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1270","DOI":"10.1016\/j.aml.2011.11.022","article-title":"Parabolic Herz spaces and their applications","volume":"25","author":"Ragusa","year":"2012","journal-title":"Appl. Math. Lett."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"475","DOI":"10.2140\/pjm.1969.30.475","article-title":"Multi-valued contraction mappings","volume":"30","author":"Nadler","year":"1969","journal-title":"Pacific J. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"4585","DOI":"10.1016\/j.na.2007.11.015","article-title":"Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point problems","volume":"69","author":"Ceng","year":"2008","journal-title":"Nonlinear Anal. TMA"},{"key":"ref_27","first-page":"91","article-title":"Regularization of non-coercive quasivariational inequalities","volume":"29","author":"Giannessi","year":"2000","journal-title":"Control Cybern."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.11650\/twjm\/1500406298","article-title":"Well-posedness of hemivariational inequalities and inclusion problems","volume":"15","author":"Xiao","year":"2011","journal-title":"Taiwanese J. Math."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1007\/s10898-014-0198-7","article-title":"Some equivalence results for well-posedness of hemivariational inequalities","volume":"61","author":"Xiao","year":"2015","journal-title":"J. Glob. Optim."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2139","DOI":"10.1016\/j.na.2011.10.013","article-title":"Levitin-Polyak well-posedness of a generalized mixed variational inequality in Banach spaces","volume":"75","author":"Li","year":"2012","journal-title":"Nonlinear Anal. TMA"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"881","DOI":"10.2298\/FIL1205881C","article-title":"Well-posedness by perturbations of variational-hemivariational inequalities with perturbations","volume":"26","author":"Ceng","year":"2012","journal-title":"Filomat"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"194509","DOI":"10.1155\/2012\/194509","article-title":"Well-posedness by perturbations of generalized mixed variational inequalities in Banach spaces","volume":"2012","author":"Ceng","year":"2012","journal-title":"J. Appl. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2798","DOI":"10.22436\/jnsa.009.05.75","article-title":"Some equivalence results for well-posedness of generalized hemivariational inequalities with Clarke\u2019s generalized directional derivative","volume":"9","author":"Ceng","year":"2016","journal-title":"J. Nonlinear Sci. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"712306","DOI":"10.1155\/2012\/712306","article-title":"Well-posedness for a class of strongly mixed variational-hemivariational inequalities with perturbations","volume":"2012","author":"Ceng","year":"2012","journal-title":"J. Appl. Math."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1341\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:40:11Z","timestamp":1760139611000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/7\/1341"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,29]]},"references-count":34,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["sym14071341"],"URL":"https:\/\/doi.org\/10.3390\/sym14071341","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,6,29]]}}}