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
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