Subject: delta-convex mapping - LINDAT/CLARIAH-CZ Catalog Search Results

Start Over Subject delta-convex mapping

Creator:: Pavlica, D.
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: Morse-Sard theorem and delta-convex mapping
Language:: English
Description:: Let f : I → X be a delta-convex mapping, where I ⊂ R is an open interval and X a Banach space. Let Cf be the set of critical points of f. We prove that f(Cf ) has zero 1/2-dimensional Hausdorff measure.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

Creator:: Veselý, Libor and Zajíček, Luděk
Format:: bez média and svazek
Type:: model:article and TEXT
Subject:: bounded convexity, delta-convex mapping, bounded variation, and Banach space
Language:: English
Description:: Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity Kb a F is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
Rights:: http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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