Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T16:26:37.487Z Has data issue: false hasContentIssue false
  • English
  • Français

Applications of Variants of the Hölder Inequality and its Inverses: Extensions of Barnes, Marshall-Olkin, and Nehari Inequalities.

Published online by Cambridge University Press:  20 November 2018

Chung-Lie Wang
Chung-Lie Wang*
Affiliation:
Dept. of Mathematics, University of Regina, Regina, Saskatchewan S4S 0A2
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The primary aim of this paper is to extend Barnes [1], Marshall-Olkin [6], and Nehari [8] inequalities as applications of some results introduced in [10] by the author.

Since several results from various sources are adopted here, a unified notation is required in order to simplify our subsequent arguments. To this end, let Lp = Lp(S, ∑, μ), p>0 (unless otherwise stated), be the space of all pth power non-negative integrable functions over a given finite measure space (S, ∑, μ) (where S may be regarded as a bounded subset of real numbers).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 21 , Issue 3 , 01 September 1978 , pp. 347 - 354
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Barnes, D. C., Some complements of Hölder's inequality. J. Math. Anal. Appl. 26 (1969), 82-87.Google Scholar
2. Bartle, R. G., The elements of integration. John Wiley and Sons, New York, 1966.Google Scholar
3. Beckenbach, E. F. and R. Bellman, Inequalities. Springer-Verlag, Berlin, 1961.Google Scholar
4. Bellman, R., Converses of Schwarz's inequality. Duke Math. J. 23 (1956), 429-434.Google Scholar
5. Hardy, G. A., Littlewood, J. E. and Polya, G., Inequalities. 2nd ed. Cambridge Univ. Press, Cambridge, 1959.Google Scholar
6. Marshall, A. W. and I. Olkin, Reversal of the Lyapunov, Holder and Minkowski inequalities and other extensions of the Kantorovich inequality. J. Math. Anal. Appl. 8 (1964), 503-514.Google Scholar
7. Mitrinovic, D. S., Analytic inequalities. Springer-Verlag, Berlin, 1970.Google Scholar
8. Nehari, Z., Inverse Hölder inequalities. J. Math. Anal. Appl. 21 (1968), 405-420.Google Scholar
9. Wang, Chung-lie, An extension of a Bellman inequality, Utilitas Mathematica, 8 (1975), 251-256.Google Scholar
10. Wang, Chung-lie. Variants of the Holder inequality and its inverses, Can. Math. Bull.,.20 (1977), 377-384.Google Scholar