No CrossRef data available.
Article contents
Inequalities and semigroups
Published online by Cambridge University Press: 17 April 2009
Abstract
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.
We define the notion of a convex function between semigroups and show that for such functions one obtains not only Jensen's Inequality but a new and powerful companion inequality. Taken together, these two inequalities can be easily applied to give trivial derivations of many of the classical inequalities as well as many new inequalities.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1989
References
[1] Hardy, G.H., Littlewood, J.E. and Polya, G., Inequalities (Cambridge Univ. Press, London and New York, 1st ed. 1934, 2nd ed. 1952).Google Scholar
[2] Kazarinoff, N.D, Analytic inequalities (Holt, Rinehart and Winston, New York, 1961).Google Scholar
[3] Klamkin, M.S., ‘Extensions of the Weeirstrass product inequalities II’, Amer. Math. Monthly 82 (1975), 741–742.Google Scholar
[4] Klamkin, M.S. and Newman, D.J., ‘Extensions of the Weierstrass product inequalities’, Math. Mag 43 (1970), 137–141.Google Scholar
[5] Levine, E. and Schaumberger, N., ‘Comparability of sin 
and ’, College Math. J. 17 (1986), 362–363.Google Scholar
and 
’, College Math. J. 17 (1986), 362–363.Google Scholar[7] Olkin, I. and Marshall, A.W., Inequalities: Theory of majorization and its applications (Academic Press, New York, 1979).Google Scholar
[8] Roberts, A.W. and Varberg, D.E., Convex functions (Academic Press, New York, 1973).Google Scholar
You have
Access