{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T06:53:35Z","timestamp":1769756015731,"version":"3.49.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T00:00:00Z","timestamp":1566777600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T00:00:00Z","timestamp":1566777600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100002261","name":"\u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u0438\u0439 \u0424\u043e\u043d\u0434 \u0424\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u0445 \u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0439","doi-asserted-by":"publisher","award":["18-01-00036 A"],"award-info":[{"award-number":["18-01-00036 A"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2021,7]]},"DOI":"10.1007\/s00454-019-00130-w","type":"journal-article","created":{"date-parts":[[2019,8,26]],"date-time":"2019-08-26T16:04:19Z","timestamp":1566835459000},"page":"273-280","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Approximate Carath\u00e9odory\u2019s Theorem in Uniformly Smooth Banach Spaces"],"prefix":"10.1007","volume":"66","author":[{"given":"Grigory","family":"Ivanov","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,8,26]]},"reference":[{"key":"130_CR1","doi-asserted-by":"crossref","unstructured":"Adiprasito, K., B\u00e1r\u00e1ny, I., Mustafa, N.H.: Theorems of Carath\u00e9odory, Helly, and Tverberg without dimension. In: Proceedings of the 30th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2350\u20132360. SIAM, Philadelphia (2019)","DOI":"10.1137\/1.9781611975482.143"},{"key":"130_CR2","doi-asserted-by":"crossref","unstructured":"Barman, S.: Approximating Nash equilibria and dense bipartite subgraphs via an approximate version of Carath\u00e9odory\u2019s theorem. In: Proceedings of the 47th Annual ACM Symposium on Theory of Computing, pp. 361\u2013369. ACM, New York (2015)","DOI":"10.1145\/2746539.2746566"},{"key":"130_CR3","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/BFb0090048","volume-title":"Geometric Aspects of Functional Analysis","author":"J Bourgain","year":"1989","unstructured":"Bourgain, J., Pajor, A., Szarek, S.J., Tomczak-Jaegermann, N.: On the duality problem for entropy numbers of operators. In: Lindenstrauss, J., Milman, V.D. (eds.) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol. 1376, pp. 50\u201363. Springer, Berlin (1989)"},{"issue":"1","key":"130_CR4","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF01449883","volume":"64","author":"C Carath\u00e9odory","year":"1907","unstructured":"Carath\u00e9odory, C.: \u00dcber den Variabilit\u00e4tsbereich der Koeffizienten von Potenzreihen, die gegebene Werte nicht annehmen. Math. Ann. 64(1), 95\u2013115 (1907)","journal-title":"Math. Ann."},{"issue":"3","key":"130_CR5","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1017\/S0305004100051884","volume":"78","author":"JWS Cassels","year":"1975","unstructured":"Cassels, J.W.S.: Measures of the non-convexity of sets and the Shapley\u2013Folkman\u2013Starr theorem. Math. Proc. Cambridge Philos. Soc. 78(3), 433\u2013436 (1975)","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"130_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0082079","volume-title":"Geometry of Banach Spaces\u2014Selected Topics. Lecture Notes in Mathematics","author":"J Diestel","year":"1975","unstructured":"Diestel, J.: Geometry of Banach Spaces\u2014Selected Topics. Lecture Notes in Mathematics, vol. 485. Springer, Berlin (1975)"},{"issue":"3\u20134","key":"130_CR7","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/BF02762802","volume":"13","author":"P Enflo","year":"1972","unstructured":"Enflo, P.: Banach spaces which can be given an equivalent uniformly convex norm. Israel J. Math. 13(3\u20134), 281\u2013288 (1972)","journal-title":"Israel J. Math."},{"key":"130_CR8","doi-asserted-by":"crossref","unstructured":"Fradelizi, M., Madiman, M., Marsiglietti, A., Zvavitch, A.: The convexification effect of Minkowski summation (2017). arXiv:1704.05486","DOI":"10.4171\/EMSS\/26"},{"issue":"1","key":"130_CR9","first-page":"26","volume":"6","author":"GM Ivanov","year":"2015","unstructured":"Ivanov, G.M.: Modulus of supporting convexity and supporting smoothness. Eurasian Math. J. 6(1), 26\u201340 (2015)","journal-title":"Eurasian Math. J."},{"issue":"3\u20134","key":"130_CR10","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1134\/S000143461209009X","volume":"92","author":"GM Ivanov","year":"2012","unstructured":"Ivanov, G.M., Polovinkin, E.S.: A generalization of the set averaging theorem. Math. Notes 92(3\u20134), 369\u2013374 (2012)","journal-title":"Math. Notes"},{"issue":"3","key":"130_CR11","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1215\/20088752-2017-0001","volume":"8","author":"G Ivanov","year":"2017","unstructured":"Ivanov, G., Martini, H.: New moduli for Banach spaces. Ann. Funct. Anal. 8(3), 350\u2013365 (2017)","journal-title":"Ann. Funct. Anal."},{"issue":"1\u20132","key":"130_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02760825","volume":"30","author":"RC James","year":"1978","unstructured":"James, R.C.: Nonreflexive spaces of type 2. Israel J. Math. 30(1\u20132), 1\u201313 (1978)","journal-title":"Israel J. Math."},{"issue":"3","key":"130_CR13","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1307\/mmj\/1028998906","volume":"10","author":"J Lindenstrauss","year":"1963","unstructured":"Lindenstrauss, J.: On the modulus of smoothness and divergent series in Banach spaces. Michigan Math. J. 10(3), 241\u2013252 (1963)","journal-title":"Michigan Math. J."},{"key":"130_CR14","unstructured":"Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II: Function Spaces. Ergebnisse der Mathematik und ihrer Grenzgebiet, vol. 97. Springer, Berlin (2013)"},{"issue":"3\u20134","key":"130_CR15","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/BF02760337","volume":"20","author":"G Pisier","year":"1975","unstructured":"Pisier, G.: Martingales with values in uniformly convex spaces. Israel J. Math. 20(3\u20134), 326\u2013350 (1975)","journal-title":"Israel J. Math."},{"key":"130_CR16","unstructured":"Pisier, G.: Remarques sur un r\u00e9sultat non publi\u00e9 de B. Maurey. In: S\u00e9minaire Analyse fonctionnelle (dit \u201cMaurey-Schwartz\u201d), vol. 5, pp. 1\u201312 (1980)"},{"key":"130_CR17","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/BFb0078146","volume-title":"Geometrical Aspects of Functional Analysis","author":"G Pisier","year":"1987","unstructured":"Pisier, G., Xu, Q.H.: Random series in the real interpolation spaces between the spaces $$v_p$$. In: Lindenstrauss, J., Milman, V.D. (eds.) Geometrical Aspects of Functional Analysis. Lecture Notes in Mathematics, vol. 1267, pp. 185\u2013209. Springer, Berlin (1987)"},{"issue":"1","key":"130_CR18","doi-asserted-by":"publisher","first-page":"25","DOI":"10.2307\/1909201","volume":"37","author":"RM Starr","year":"1969","unstructured":"Starr, R.M.: Quasi-equilibria in markets with non-convex preferences. Econometrica 37(1), 25\u201338 (1969)","journal-title":"Econometrica"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00130-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00454-019-00130-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-019-00130-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,9]],"date-time":"2021-06-09T15:08:17Z","timestamp":1623251297000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00454-019-00130-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,26]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["130"],"URL":"https:\/\/doi.org\/10.1007\/s00454-019-00130-w","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,26]]},"assertion":[{"value":"15 April 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 July 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 August 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 August 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}