Inequalities involving multivariate convex functions. II
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- by Edward Neuman PDF
- Proc. Amer. Math. Soc. 109 (1990), 965-974 Request permission
Abstract:
In this paper we offer some inequalities involving multivariate convex functions. Among other things a refinement of classical Jensen’s inequality as well as an extension of Fejér’s inequality to the case of $s$-variate $(s \geq 1)$ functions are included. These results are obtained with the aid of the generalized simplex splines.References
-
C. de Boor, Splines as linear combinations of $B$-splines: a survey, in Approximation Theory II (G. G. Lorentz, C. K. Chui, and L. L. Schumaker, eds.), Academic Press, New York, 1976, pp. 1-47.
- B. C. Carlson, A hypergeometric mean value, Proc. Amer. Math. Soc. 16 (1965), 759–766. MR 179389, DOI 10.1090/S0002-9939-1965-0179389-6
- Billie Chandler Carlson, Special functions of applied mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0590943
- Wolfgang Dahmen and Charles A. Micchelli, Recent progress in multivariate splines, Approximation theory, IV (College Station, Tex., 1983) Academic Press, New York, 1983, pp. 27–121. MR 754343 —, Statistical encounters with $B$-splines, Contemp. Math. 59 (1986), 17-48. L. Fejér, Über die Fourierreihen II, Math. Naturwiss. Anz. Ungar. Akad. Wiss. 24 (1906), 369-390.
- S. Karlin, C. A. Micchelli, and Y. Rinott, Multivariate splines: a probabilistic perspective, J. Multivariate Anal. 20 (1986), no. 1, 69–90. MR 862242, DOI 10.1016/0047-259X(86)90020-5
- E. J. McShane, Jensen’s inequality, Bull. Amer. Math. Soc. 43 (1937), no. 8, 521–527. MR 1563579, DOI 10.1090/S0002-9904-1937-06588-8
- D. S. Mitrinović and I. B. Lacković, Hermite and convexity, Aequationes Math. 28 (1985), no. 3, 229–232. MR 791622, DOI 10.1007/BF02189414
- Edward Neuman and Josip Pe arić, Inequalities involving multivariate convex functions, J. Math. Anal. Appl. 137 (1989), no. 2, 541–549. MR 984976, DOI 10.1016/0022-247X(89)90262-X
- A. Wayne Roberts and Dale E. Varberg, Convex functions, Pure and Applied Mathematics, Vol. 57, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0442824
- E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. MR 1424469, DOI 10.1017/CBO9780511608759
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 965-974
- MSC: Primary 26D99; Secondary 41A15
- DOI: https://doi.org/10.1090/S0002-9939-1990-1009996-4
- MathSciNet review: 1009996