Variants of the Hölder Inequality and its Inverses
Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 377-384

Voir la notice de l'article provenant de la source Cambridge University Press

This paper presents variants of the Holder inequality for integrals of functions (as well as for sums of real numbers) and its inverses. In these contexts, all possible transliterations and some extensions to more than two functions are also mentioned.
Wang, Chung-Lie. Variants of the Hölder Inequality and its Inverses. Canadian mathematical bulletin, Tome 20 (1977) no. 3, pp. 377-384. doi: 10.4153/CMB-1977-056-5
@article{10_4153_CMB_1977_056_5,
     author = {Wang, Chung-Lie},
     title = {Variants of the {H\"older} {Inequality} and its {Inverses}},
     journal = {Canadian mathematical bulletin},
     pages = {377--384},
     year = {1977},
     volume = {20},
     number = {3},
     doi = {10.4153/CMB-1977-056-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-056-5/}
}
TY  - JOUR
AU  - Wang, Chung-Lie
TI  - Variants of the Hölder Inequality and its Inverses
JO  - Canadian mathematical bulletin
PY  - 1977
SP  - 377
EP  - 384
VL  - 20
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-056-5/
DO  - 10.4153/CMB-1977-056-5
ID  - 10_4153_CMB_1977_056_5
ER  - 
%0 Journal Article
%A Wang, Chung-Lie
%T Variants of the Hölder Inequality and its Inverses
%J Canadian mathematical bulletin
%D 1977
%P 377-384
%V 20
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1977-056-5/
%R 10.4153/CMB-1977-056-5
%F 10_4153_CMB_1977_056_5

[1] 1. Bartle, R. G., The elements of integration, John-Wiley and Sons, New York, 1966. Google Scholar

[2] 2. Beckenbach, E. F. and Bellman, R., Inequalities, Springer-Verlag, Berlin, 1961. Google Scholar

[3] 3. Chung, K. L., A course in probability theory. Harcourt, Brace & World, Inc., New York, 1968. Google Scholar

[4] 4. Diaz, J. B. and Metcalf, F. T.. Complementary inequalities I: Inequalities complementary to Cauchy's inequality for sums of real numbers, J. Math. Anal, and Appl. 9 (1964), 59-74. Google Scholar

[5] 5. Diaz, J. B. and Metcalf, F. T., Complementary inequalities II: Inequalities complementary to the Buniakowsky-Schwarz inequality for integrals, J. Math. Anal, and Appl. 9 (1964), 278-293. Google Scholar

[6] 6. Diaz, J. B. and Metcalf, F. T., Stronger forms of a class of inequalities of G. Pόlya-G. Szegö and Kantorovich, Bull. Amer. Math. Soc. 69 (1963), 415-418. Google Scholar

[7] 7. Diaz, J. B., Goldman, A. J., and Metcalf, F. T., Equivalence of certain inequalities complementing those of Cauchy-Schwarz and Holder, J. Res. NBS 68B (Math, and Math. Phys.) No. 2 (1964), 147-149. Google Scholar

[8] 8. Dunford, N. and Schwartz, J. T., Linear operators Part I: General Theory, Interscience, New York, 1958. Google Scholar

[9] 9. Greub, W. and Rheinboldt, W., On a generalization of an inequality of L. V. Kantorovich, Proc. America Math. Soc. 10 (1959), 407-415. Google Scholar

[10] 10. Kantorovich, L. V., Functional analysis and applied mathematics, Uspehi Mat. Nauk 3 (1948), 89-185 (also translated from the Russian by C. D. Benster, Nat. Bur. Standards Report No. 1509, 1952). Google Scholar

[11] 11. Munroe, M. E., Introduction to measure and integration, Addison-Wesley, Reading, Mass., 1953. Google Scholar

[12] 12. Pόlya, G. and Szegö, G., Aufgaben und Lehrsätze aus der Analysis, Vol. I. Berlin, 1925. Google Scholar

[13] 13. Schweitzer, P., Egy egyenlotlenség ax aritmetikai középértékröl (An inequality concerning the arithmetic mean), Math, es phys. lopok 23 (1914), 257-261. Google Scholar

[14] 14. Wang, Chung-Lie, An extension of a Bellman inequality, Utilitas mathematica, 8 (1975), 251-256. Google Scholar

Cité par Sources :