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ON THE MODULUS OF CONTINUITY OF MAPPINGS BETWEEN EUCLIDEAN SPACES
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 112, no 1, 147-160 p.Article in journal (Refereed) Published
Abstract [en]

Let f be a function from R-P to R-q and let Lambda be a finite set of pairs (theta, eta) is an element of R-P x R-q. Assume that the real-valued function (eta, f(x)) is Lipschitz continuous in the direction theta for every (theta, eta) is an element of Lambda. Necessary and sufficient conditions on Lambda are given for this assumption to imply each of the following: (1) that f is Lipschitz continuous, and (2) that f is continuous with modulus of continuity <= C epsilon vertical bar log epsilon vertical bar.

Place, publisher, year, edition, pages
2013. Vol. 112, no 1, 147-160 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-92051ISI: 000319844000010OAI: oai:DiVA.org:su-92051DiVA: diva2:636947
Note

AuthorCount:2;

Available from: 2013-07-15 Created: 2013-07-15 Last updated: 2017-12-06Bibliographically approved

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