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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Smoothness properties of generalized convex functions

Author: R. A. Zalik
Journal: Proc. Amer. Math. Soc. 56 (1976), 118-120
MSC: Primary 26A51
MathSciNet review: 0419700
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Abstract: 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.

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  • [1] Samuel Karlin and William J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Applied Mathematics, Vol. XV, Interscience Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0204922
  • [2] I. P. Nathanson, Theory of functions of a real variable, vol. II, GITTL, Moscow, 1957; English transl. of 2nd rev. ed., Ungar, New York, 1961. MR 26 #6309.
  • [3] G. Mühlbach, A recurrence formula for generalized divided differences and some applications, J. Approximation Theory 9 (1973), 165–172. MR 0353623
  • [4] R. A. Zalik, Existence of Tchebycheff extensions, J. Math. Anal. Appl. 51 (1975), 68–75. MR 0372507

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Article copyright: © Copyright 1976 American Mathematical Society