Properties of functions generalized convex with respect to a WT-system

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Smoothness Properties of Generalized Convex Functions

We present a concise and elementary proof of a theorem of Karlin and Studden concerning the smoothness properties of functions belonging to a generalized convexity cone. In [1, Chapter XI], Karlin and Studden showed that a function which is convex with respect to an extended complete Tchebycheff system has a continuous derivative of order n — 1, a fact which is of considerable importance in the...

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ژورنال

عنوان ژورنال: Journal of Approximation Theory

سال: 1981

ISSN: 0021-9045

DOI: 10.1016/0021-9045(81)90062-9