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On Knopp's Inequality for Convex Functions

Published online by Cambridge University Press:  20 November 2018

J. E. Pečarić  and
P. R. Beesack
J. E. Pečarić
Affiliation:
University Of Belgrade Bulevar Revolucije 73 11000 Belgrade, Yugoslavia
P. R. Beesack
Affiliation:
Carleton university ottawa, ont., canada
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Abstract

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Knopp's inequality for convex functions ϕ on an interval I = [m,M] states that

for an explicit functional H, and all integrable g: [0, 1] → I. In this paper we give results of this kind in which the integral operator, ∫, is replaced by a general isotonic linear functional.

Keywords

Primary 26D15Secondary 26D2047B38
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 3 , 01 September 1987 , pp. 267 - 272
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Beck, E., Komplementare Ungleichungen bei vergleichbaren Mittelwerten, Montash. für Math. 73 (1969), pp. 289–308.Google Scholar
2. Beesack, P.R., On inequalities complementary to Jensen's, Can. J. Math. 35 (1983), pp. 324–338.Google Scholar
3. Beesack, P.R. and Pečarić, J.E., OnJessen's inequality for convex functions, J. Math. Anal. Appl. 110 (1985), pp. 536–552.Google Scholar
4. Grüss, G., Über das Maximum des absoluten Betrages von Math. Zeit. 39 (1935), pp. 215–226.Google Scholar
5. Knopp, K., Über die maximalen Abstde una Verhältnisse verschiedener Mittelwerte, Math. Zeit. 39 (1935), pp. 768–776.Google Scholar
6. Mitrinović, D.S., Bullen, P.S. and Vasić, P.M., Sredine i sa njima povezane nejednakosti, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 600 (1977), pp. 1–232.Google Scholar
7. Mitrinović, D.S., Analytic Inequalities, Berlin-Heidelberg-New York, 1970.Google Scholar
8. Mitrinović, D.S. and Vasić, P.M., The centroid method in inequalities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 498-541 (1975), pp. 3–16.Google Scholar
9. Popoviciu, T., Les Fonctions Convexes, Paris, 1944.Google Scholar