On a refinement of the Majorisation type inequality

• Autorzy: Adil Khan, M. , Niezgoda, M. , Pečarić, J.
• Języki publikacji: EN

Abstrakty

EN

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

EN

convex function; log-convexity; Cauchy means

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 1
• Strony: 49-57
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Adil Khan, M.

• Abdus Salam School of Mathematical Sciences Gc University, Lahore, Pakistan,

autor

Niezgoda, M.

• Department of Applied Mathematics and Computer Science University of Life Sciences in Lublin 20-950 Lublin, Poland,

autor

Pečarić, J.

• 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