Geodesic
On vector functions of bounded convexity
Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 321-335

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Let $X$ be a normed linear space. We investigate properties of vector functions $F\colon [a,b] \to X$ of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity $K_a^b F$ 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 As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
Let $X$ be a normed linear space. We investigate properties of vector functions $F\colon [a,b] \to X$ of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity $K_a^b F$ 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 As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.
DOI : 10.21136/MB.2008.140621
Classification : 26A99, 47H99
Keywords: bounded convexity; delta-convex mapping; bounded variation; Banach space 
Veselý, Libor; Zajíček, Luděk. On vector functions of bounded convexity. Mathematica Bohemica, Tome 133 (2008) no. 3, pp. 321-335. doi: 10.21136/MB.2008.140621
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