- citati u SCIndeksu: 0
- citati u CrossRef-u:0
- citati u Google Scholaru:[
 ]
- posete u poslednjih 30 dana:9
- preuzimanja u poslednjih 30 dana:7
|
|
|
2018, vol. 22, br. 2, str. 59-67
|
A note on the proofs of generalized Radon inequality
(naslov ne postoji na srpskom)
aCentral South University Changsha, School of Mathematics and Statistics, Hunan, P.R. China bSouthwestern University of Finance and Economic Chengdu, Institute of Mathematics, School of Economic Mathematics, Sichuan, P.R. China cZhejiang University, School of Mathematical Sciences, Hangzhou, Zhejiang, P.R. China
e-adresa: yli777@qq.com, guxianming@live.cn, jcxshaw@outlook.com
Ključne reči: the Bergström inequality; the Radon inequality; the weighted power mean inequality; equivalence; the Hölder inequality
Sažetak
(ne postoji na srpskom)
In this paper, we introduce and prove several generalizations of the Radon inequality. The proofs in the current paper unify and also are simpler than those in early published work. Meanwhile, we find and show the mathematical equivalences among the Bernoulli inequality, the weighted AM-GM inequality, the Hölder inequality, the weighted power mean inequality and the Minkowski inequality. Finally, some applications involving the results proposed in this work are shown.
|
|
|
|
Reference
|
|
  
|
Abramovich, S., Mond, B., Pečarić, J.E. (1997) Sharpening Jensen's Inequality and a Majorization Theorem. Journal of Mathematical Analysis and Applications, 214(2): 721-728
|
|
|
Batinetu-Giurgiu, D.M., Pop, O.T. (2010) A generalization of Radon's inequality. Creative Mathematics and Informatics, 19 (2); 116-121
|
|
|
Bellman, R. (1955) Notes on Matrix Theory--IV (An Inequality Due to Bergstrom). American Mathematical Monthly, 62(3): 172
|
|
|
Bergström, H. (1952) A triangle inequality for matrices. u: Den Elfte Skandinaviske Matematikerkongress, Trondheim, 1949, Oslo: Johan Grundt Tanums Forlag, 264-267
|
|
|
Cvetkovski, Z. (2012) Inequalities. Theorems, Techniques and Selected Problems. Heidelberg: Springer- Verlag Berlin Heidelberg
|
|
|
Fan, K. (1959) Generalization of Bergsrröm inequality. American Mathematical Monthly, 66(2): 153
|
|
|
Hardy, G.H., Littlewood, J.E., Pólya, G. (1934) Inequalities. Cambridge, UK: Cambridge University Press
|
|
|
Li, Y., Gu, X., Zhao, J. (2018) The Weighted Arithmetic Mean-Geometric Mean Inequality is Equivalent to the Hölder Inequality. Symmetry, 10(9): 380
|
|
|
Maligranda, L. (2001) Equivalence of the Hölder-Rogers and Minkowski Inequalities. Mathematical Inequalities & Applications, (2): 203-207
|
|
|
Manfrino, R.B., Gómez, O.J.A., Delgado, R.V. (2009) Inequalities. Basel: Springer Nature
|
|
|
Mitrinovic, D.S., Pecaric, J.E., Fink, A.M. (1993) Classical and New Inequalities in Analysis. u: Mathematics and Its Applications (East European Series), Dordrecht: Kluwer Amcademic, Vol. 61
|
|
|
Morrey, C.B. (1933) A Class of Representations of Manifolds. Part I. American Journal of Mathematics, 55(1/4): 683
|
|
|
Mortici, C. (2011) A new refinement of the Radon inequality. Mathematical Communications, 16 (2); 319-324
|
|
|
Pecaric, J.E., Proschan, F., Tong, Y.I. (1992) Convex Functions, Partial Orderings, and Statistical Applications, Mathematics in Science and Engineering. San Diego, CA: Academic Press
|
|
|
Radon, J. (1913) Über die absolut additiven Mengenfunktionen. Wiener Sitzungsber, (IIa), 122, 1295-1438
|
|
|
Yang, K-C. (2002) A note and generalization of a fractional inequality. Journal of Yueyang Normal University, Natural Science Edition, in Chinese, 15 (4); 9-11
|
|
|
|
|