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We prove their H\u00f6lder continuity and establish explicit expressions for the corresponding constants. We show that these constants are optimal for odd derivatives and at most two times suboptimal for the even ones. In the particular case of integer powers, when the H\u00f6lder continuity transforms into the Lipschitz continuity, we improve this result and obtain the optimal constants.<\/jats:p>","DOI":"10.1007\/s10957-020-01653-6","type":"journal-article","created":{"date-parts":[[2020,3,27]],"date-time":"2020-03-27T13:02:55Z","timestamp":1585314175000},"page":"303-326","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Smoothness Parameter of Power of Euclidean Norm"],"prefix":"10.1007","volume":"185","author":[{"given":"Anton","family":"Rodomanov","sequence":"first","affiliation":[]},{"given":"Yurii","family":"Nesterov","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,3,27]]},"reference":[{"issue":"1","key":"1653_CR1","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/s10107-006-0706-8","volume":"108","author":"Y Nesterov","year":"2006","unstructured":"Nesterov, Y., Polyak, B.T.: Cubic regularization of Newton method and its global performance. 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