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Displaying similar documents to “On P - and p -convexity of Banach spaces.”

On vector functions of bounded convexity

Libor Veselý, Luděk Zajíček (2008)

Mathematica Bohemica

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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 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 As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.