{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:54:04Z","timestamp":1773795244265,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2022,1,11]],"date-time":"2022-01-11T00:00:00Z","timestamp":1641859200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,11]],"date-time":"2022-01-11T00:00:00Z","timestamp":1641859200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s10957-021-01966-0","type":"journal-article","created":{"date-parts":[[2022,1,11]],"date-time":"2022-01-11T18:46:43Z","timestamp":1641926803000},"page":"21-41","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Variational Principles and Mean Value Estimates"],"prefix":"10.1007","volume":"193","author":[{"given":"A. V.","family":"Arutyunov","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2686-4654","authenticated-orcid":false,"given":"S. E.","family":"Zhukovskiy","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,1,11]]},"reference":[{"issue":"3","key":"1966_CR1","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1134\/S1064562420030035","volume":"101","author":"AN Agadzhanov","year":"2020","unstructured":"Agadzhanov, A.N.: On some properties of superreflexive besov spaces. Dokl. Math. 101(3), 177\u2013181 (2020)","journal-title":"Dokl. Math."},{"key":"1966_CR2","doi-asserted-by":"crossref","unstructured":"Alekseev, V.M., Tikhomirov, V.M., Fomin, S.V.: Optimal control. Contemporary Soviet Mathematics, Consultants Bureau, New York (1987)","DOI":"10.1007\/978-1-4615-7551-1"},{"issue":"2","key":"1966_CR3","doi-asserted-by":"publisher","first-page":"994","DOI":"10.1137\/18M1164287","volume":"29","author":"AV Arutyunov","year":"2019","unstructured":"Arutyunov, A.V., Zhukovskiy, S.E.: Variational principles in analysis and existence of minimizers for functions on metric spaces. SIAM J. Optim. 29(2), 994\u20131016 (2019)","journal-title":"SIAM J. Optim."},{"key":"1966_CR4","volume-title":"Applied Nonlinear Analysis","author":"JP Aubin","year":"1984","unstructured":"Aubin, J.P., Ekeland, I.: Applied Nonlinear Analysis. Wiley, NY (1984)"},{"issue":"3+4","key":"1966_CR5","first-page":"477","volume":"13","author":"D Az\u00e8","year":"2006","unstructured":"Az\u00e8, D., Corvellec, J.-N.: Variational methods in classical open mapping theorems. J. Convex Anal. 13(3+4), 477\u2013488 (2006)","journal-title":"J. Convex Anal."},{"key":"1966_CR6","first-page":"531","volume":"36","author":"TQ Bao","year":"2007","unstructured":"Bao, T.Q., Mordukhovich, B.S.: Variational principles for set-valued mappings with applications to multiobjective optimization. Control. Cybern. 36, 531\u2013562 (2007)","journal-title":"Control. Cybern."},{"key":"1966_CR7","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/s00013-009-0072-x","volume":"93","author":"EM Bednarczuk","year":"2009","unstructured":"Bednarczuk, E.M., Zagrodny, D.: Vector variational principle. Arch. Math. 93, 577\u2013586 (2009)","journal-title":"Arch. Math."},{"key":"1966_CR8","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF01581072","volume":"57","author":"JM Borwein","year":"1992","unstructured":"Borwein, J.M., Lewis, A.S.: Partially finite convex programming, part I: quasi relative interiors and duality theory. Math. Program. 57, 15\u201348 (1992)","journal-title":"Math. Program."},{"key":"1966_CR9","volume-title":"Techniques of Variational Analysis","author":"JM Borwein","year":"2005","unstructured":"Borwein, J.M., Zhu, Q.J.: Techniques of Variational Analysis. Springer, NY (2005)"},{"issue":"4","key":"1966_CR10","doi-asserted-by":"publisher","first-page":"1075","DOI":"10.1090\/S0002-9939-1994-1212282-4","volume":"122","author":"F Clarke","year":"1994","unstructured":"Clarke, F., Ledyaev, Yu.S.: Mean value inequalities. Proc. Am. Math. Soc. 122(4), 1075\u20131083 (1994)","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"1966_CR11","first-page":"75","volume":"48","author":"F Clarke","year":"1994","unstructured":"Clarke, F., Ledyaev, Yu.S.: New formulas for finite increments. Dokl. Math. 48(1), 75\u201379 (1994)","journal-title":"Dokl. Math."},{"key":"1966_CR12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971309","volume-title":"Optimization and Nonsmooth Analysis","author":"FH Clarke","year":"1990","unstructured":"Clarke, F.H.: Optimization and Nonsmooth Analysis. SIAM, Philadelphia (1990)"},{"key":"1966_CR13","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s11228-010-0133-0","volume":"18","author":"MJ Fabian","year":"2010","unstructured":"Fabian, M.J., Henrion, R., Kruger, A.Y., et al.: Error bounds: necessary and sufficient conditions. Set-Valued Anal. 18, 121\u2013149 (2010)","journal-title":"Set-Valued Anal."},{"key":"1966_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21593-8","volume-title":"Fixed Point Theory","author":"A Granas","year":"2003","unstructured":"Granas, A., Dugundji, J.: Fixed Point Theory. Springer, New York (2003)"},{"key":"1966_CR15","volume-title":"Positive Solutions of Operator Equations","author":"MA Krasnosel\u2018skii","year":"1964","unstructured":"Krasnosel\u2018skii, M.A.: Positive Solutions of Operator Equations. P. Noordhoff Ltd, Groningen (1964)"},{"key":"1966_CR16","first-page":"229","volume":"198","author":"IE Leonard","year":"1974","unstructured":"Leonard, I.E., Sundaresan, K.: Geometry of Lebesgue-Bochner Function Spaces-Smoothness. Trans. AMS 198, 229\u2013251 (1974)","journal-title":"Trans. AMS"},{"key":"1966_CR17","volume-title":"Iterative Solutions of Nonlinear Equations in Several Variables","author":"J Ortega","year":"1970","unstructured":"Ortega, J., Rheinboldt, W.: Iterative Solutions of Nonlinear Equations in Several Variables. McGraw-Hill, New York (1970)"},{"key":"1966_CR18","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1016\/0022-247X(79)90240-3","volume":"72","author":"R Rao Chiwkula","year":"1979","unstructured":"Rao Chiwkula, R.: Finite representation of banach spaces-smoothness. J. Math. Anal. Appl. 72, 435\u2013445 (1979)","journal-title":"J. Math. Anal. Appl."}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01966-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10957-021-01966-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-021-01966-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T19:34:13Z","timestamp":1652556853000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10957-021-01966-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,11]]},"references-count":18,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["1966"],"URL":"https:\/\/doi.org\/10.1007\/s10957-021-01966-0","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,1,11]]},"assertion":[{"value":"14 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 January 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}