Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-27T16:08:24.472Z Has data issue: false hasContentIssue false
  • English
  • Français

A continuous analogue and an extension of Radó's formulæ

Published online by Cambridge University Press:  17 April 2009

C.E.M. Pearce  and
J. pečarić
C.E.M. Pearce
Affiliation:
Applied Mathematics DepartmentThe University of AdelaideAdelaide, SA 5005Australia
J. pečarić
Affiliation:
Faculty of Textile TechnologyUniversity of ZagrebZagrebCroatia
Rights & Permissions [Opens in a new window]

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.

A continuous analogue is derived for Radó's comparison formulæ. The analogue is then employed to provide a result which continues Radó's result and interpolates an inequality of Pittenger.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 229 - 233
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Alzer, H., ‘Ungleichungen für (e/a)a (b/e)b’, Elem. Math. 40 (1985), 120–123.Google Scholar
[2]Hartman, P., ‘Convex functions and mean value inequalities’, Duke Math. J. 39 (1972), 351–360.CrossRefGoogle Scholar
[3]Imoru, C.O., ‘The power mean and the logarithmic mean’, Internat. J. Math. Math. Sci. 5 (1982), 337–343.CrossRefGoogle Scholar
[4]Kazarinoff, N.D., Analytic inequalities (Holt, New York, 1961).Google Scholar
[5]Lin, T.P., ‘The power mean and the logarithmic mean’, Amer. Math. Monthly 81 (1979), 879–883.CrossRefGoogle Scholar
[6]Lupaş, A. and Lupaş, L., ‘A class of inequalities for convex functions’, Rev. Mat. elev. Timişoara 17 (1986), 11–23.Google Scholar
[7]Pittenger, A.O., ‘Inequalities between arithmetic and logarithmic means’, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 678–715 (1980), 15–18.Google Scholar
[8]Radó, T., ‘On convex functions’, Trans. Amer. Math. Soc. 37 (1935), 266–285.CrossRefGoogle Scholar
[9]Sándor, J., ‘On the identric and logarithmic means’, Aeqationes Math. 40 (1990), 261–270.CrossRefGoogle Scholar
[10]Stolarsky, K.B., ‘The power and generalized logarithmic mean’, Amer. Math. Monthly 87 (1980), 545–548.CrossRefGoogle Scholar
[11]Székely, J.G., ‘A probabilistic proof of inequalities of some means’, Periodica Polyiech. Chem. Eng. 16 (1979), 99–101.Google Scholar
[12]Székely, J.G., ‘A classification of means’, Ann. Univ. Sci. Budapest Eötvös Sect. Math. 18 (1975/1976), 129–133.Google Scholar