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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Smoothness properties of generalized convex functions
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by R. A. Zalik PDF
Proc. Amer. Math. Soc. 56 (1976), 118-120 Request permission

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.
References
  • 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
  • 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.
  • G. Mühlbach, A recurrence formula for generalized divided differences and some applications, J. Approximation Theory 9 (1973), 165–172. MR 353623, DOI 10.1016/0021-9045(73)90104-4
  • R. A. Zalik, Existence of Tchebycheff extensions, J. Math. Anal. Appl. 51 (1975), 68–75. MR 372507, DOI 10.1016/0022-247X(75)90141-9
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 56 (1976), 118-120
  • MSC: Primary 26A51
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0419700-9
  • MathSciNet review: 0419700