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In this note, two mean value theorems are proved by using some recent results by Barnett et al. [N. S. Barnett, P. Cerone, S. S. Dragomir, Majorisation inequalities for Stieltjes integrals, Appl. Math. Lett. 22 (2009), 416-421]. A new class of Cauchy type means for two functions is studied. Logarithmic convexity for differences of power means is proved. Monotonicity of Cauchy means is shown.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
49--57
Opis fizyczny
Bibliogr. 5 poz.
Twórcy
autor
- Abdus Salam School of Mathematical Sciences Gc University, Lahore, Pakistan
autor
- Department of Applied Mathematics and Computer Science University of Life Sciences in Lublin 20-950 Lublin, Poland
autor
- University of Zagreb Faculty of Textile Technology Zagreb, Croatia
Bibliografia
- [1] N. S. Barnett, P. Cerone, S. S. Dragomir, Majorisation inequalities for Stieltjes integrals, Appl. Math. Lett. 22 (2009), 416–421.
- [2] A. W. Marshall, I. Olkin, Inequalities: Theory of Majorization and its Applications, Academic Press, New York, 1979.
- [3] J. E. Pečarić, F. Proschan, Y. C. Tong, Convex functions, Partial Orderings and Statistical Applications, Academic Press, New York, 1992.
- [4] J. E. Pečarić, A. U. Rehman, On logarithmic convexity for power sums and related results, J. Inequal. Appl. vol. 2008, Article ID 389410, 9 pages, 2008. doi:10.1155/2008/389410.
- [5] S. Simic, On logarithmic convexity for differences of power means, J. Inequal. Appl. vol. 2007, Article ID 37359, 8 pages, 2007. doi:10.1155/2007/37359
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0031-0022