{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T11:37:43Z","timestamp":1776685063986,"version":"3.51.2"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,11,11]],"date-time":"2009-11-11T00:00:00Z","timestamp":1257897600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2010,5]]},"DOI":"10.1007\/s10107-009-0316-3","type":"journal-article","created":{"date-parts":[[2009,11,10]],"date-time":"2009-11-10T07:29:56Z","timestamp":1257838196000},"page":"241-252","source":"Crossref","is-referenced-by-count":30,"title":["Towards variational analysis in metric spaces: metric regularity and fixed points"],"prefix":"10.1007","volume":"123","author":[{"given":"A. D.","family":"Ioffe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,11,11]]},"reference":[{"issue":"2","key":"316_CR1","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1134\/S1064562407050079","volume":"76","author":"A.V. Arutyunov","year":"2007","unstructured":"Arutyunov A.V.: Covering mappings in metric spaces and fixed points (in Russian). Russian Mathematics, Doklady 76(2), 665\u2013668 (2007)","journal-title":"Russian Mathematics, Doklady"},{"key":"316_CR2","unstructured":"Arutyunov, A., Avakov, E., Dmitruk, A., Gelman, B., Obukhovskii, V.V.: Locally covering maps in metric spaces and coincidence points, preprint (2007)"},{"key":"316_CR3","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/BF02771543","volume":"8","author":"H. Covitz","year":"1970","unstructured":"Covitz H., Nadler S.B. Jr: Multi-valued contraction mappings in generalized metric spaces. Israel J. Math. 8, 5\u201311 (1970)","journal-title":"Israel J. Math."},{"issue":"6","key":"316_CR4","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1070\/RM1980v035n06ABEH001973","volume":"35","author":"A.V. Dmitruk","year":"1980","unstructured":"Dmitruk A.V., Milyutin A.A., Osmolovskii N.P.: Ljusternik\u2019s theorem and the theory of extrema. Russian Math. Surveys 35(6), 11\u201351 (1980)","journal-title":"Russian Math. Surveys"},{"key":"316_CR5","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1090\/S0002-9947-02-03088-X","volume":"355","author":"A.L. Dontchev","year":"2003","unstructured":"Dontchev A.L., Lewis A.S., Rockafellar R.T.: The radius of metric regularity. Trans. Amer. Math. Soc. 355, 493\u2013517 (2003)","journal-title":"Trans. Amer. Math. Soc."},{"key":"316_CR6","volume-title":"Differential Topology","author":"V. Guillemin","year":"1976","unstructured":"Guillemin V., Pollack A.: Differential Topology. Prentice Hall, Englewood Cliffs, NJ (1976)"},{"key":"316_CR7","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1016\/0362-546X(87)90073-3","volume":"11","author":"A.D. Ioffe","year":"1987","unstructured":"Ioffe A.D.: On the local surjection property. Nonlinear Anal. TMA 11, 565\u2013592 (1987)","journal-title":"Nonlinear Anal. TMA"},{"key":"316_CR8","doi-asserted-by":"crossref","unstructured":"Ioffe, A.D.: Metric regularity and subdifferential calculus, Uspehi Mat. Nauk 55(3):103--162 (2000), (in Russian), English translation: Russian Math. Surveys, 55(3): 501--558 (2000)","DOI":"10.1070\/RM2000v055n03ABEH000292"},{"key":"316_CR9","doi-asserted-by":"crossref","unstructured":"Ioffe, A.D.: On regularity concepts in variational analysis. J. Fixed Point Theory Appl. (2010) (to appear)","DOI":"10.1007\/s11784-010-0021-0"},{"key":"316_CR10","unstructured":"Ioffe, A.D., Tikhomirov, V.M.: Theory of Extremal Problems, Nauka, Moscow (1974) (in Russian), English translation: North Holland (1979)"},{"key":"316_CR11","doi-asserted-by":"crossref","unstructured":"Mordukhovich, B.S.: Variational Analysis and Generalized Differentiation, vol. 1. Springer (2006)","DOI":"10.1007\/3-540-31247-1"},{"key":"316_CR12","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1287\/moor.5.1.43","volume":"5","author":"S.M. Robinson","year":"1980","unstructured":"Robinson S.M.: Strongly regular generalized equations. Math. Oper. Res. 5, 43\u201362 (1980)","journal-title":"Math. Oper. Res."},{"key":"316_CR13","doi-asserted-by":"crossref","unstructured":"Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer (1998)","DOI":"10.1007\/978-3-642-02431-3"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0316-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10107-009-0316-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-009-0316-3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T09:50:07Z","timestamp":1559123407000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10107-009-0316-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,11]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,5]]}},"alternative-id":["316"],"URL":"https:\/\/doi.org\/10.1007\/s10107-009-0316-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,11]]}}}