×

Jensen type inequalities involving homogeneous polynomials. (English) Zbl 1193.26024


MSC:

26D15 Inequalities for sums, series and integrals

References:

[1] Bullen PS, Mitrinović PS, Vasić PM: Means and Their Inequalities. Reidel, Dordrecht, The Netherlands; 1988. · Zbl 0687.26005 · doi:10.1007/978-94-017-2226-1
[2] Minc H: Permanents, Encyclopedia of Mathematics and Its Applications. Volume 9999. Addison-Wesley, Reading, Mass, USA; 1978:xviii+205. · Zbl 0401.15005
[3] Timofte V: On the positivity of symmetric polynomial functions. I. General results. Journal of Mathematical Analysis and Applications 2003, 284(1):174-190. 10.1016/S0022-247X(03)00301-9 · Zbl 1031.05130 · doi:10.1016/S0022-247X(03)00301-9
[4] Wen J-J, Wang W-L: Chebyshev type inequalities involving permanents and their applications. Linear Algebra and Its Applications 2007, 422(1):295-303. 10.1016/j.laa.2006.10.014 · Zbl 1117.15020 · doi:10.1016/j.laa.2006.10.014
[5] Pečarić J, Svrtan D: New refinements of the Jensen inequalities based on samples with repetitions. Journal of Mathematical Analysis and Applications 1998, 222(2):365-373. 10.1006/jmaa.1997.5839 · Zbl 0912.26008 · doi:10.1006/jmaa.1997.5839
[6] Xiao Z-G, Srivastava HM, Zhang Z-H: Further refinements of the Jensen inequalities based upon samples with repetitions. Mathematical and Computer Modelling 2010, 51(5-6):592-600. · Zbl 1190.26031 · doi:10.1016/j.mcm.2009.11.004
[7] Gao C, Wen J: Inequalities of Jensen-Pečarić-Svrtan-Fan type. Journal of Inequalities in Pure and Applied Mathematics 2008, 9(3, article 74):-8. · Zbl 1163.26332
[8] Chen Y-X, Luo J-Y, Yang J-K: A class of Jensen inequalities for homogeneous and symmetric polynomials. Journal of Sichuan Normal University 2007, 30: 481-484. · Zbl 1150.26328
[9] Wen J-J, Cheng SS, Gao C: Optimal sublinear inequalities involving geometric and power means. Mathematica Bohemica 2009, 134(2):133-149. · Zbl 1212.26079
[10] Wen, J-J; Wang, W-L, The optimization for the inequalities of power means, No. 2006, 25 (2006) · Zbl 1133.26324
[11] Yang L, Feng Y, Yao Y: A class of mechanically decidable problems beyond Tarski’s model. Science in China. Series A 2007, 50(11):1611-1620. 10.1007/s11425-007-0090-8 · Zbl 1133.68423 · doi:10.1007/s11425-007-0090-8
[12] Jensen WV: Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta Mathematica 1906, 30(1):175-193. 10.1007/BF02418571 · JFM 37.0422.02 · doi:10.1007/BF02418571
[13] Mond B, Pečarić JE: Generalization of a matrix inequality of Ky Fan. Journal of Mathematical Analysis and Applications 1995, 190(1):244-247. 10.1006/jmaa.1995.1074 · Zbl 0829.15015 · doi:10.1006/jmaa.1995.1074
[14] Wen J-J, Wang W-L: Inequalities involving generalized interpolation polynomials. Computers & Mathematics with Applications 2008, 56(4):1045-1058. 10.1016/j.camwa.2008.01.032 · Zbl 1155.26310 · doi:10.1016/j.camwa.2008.01.032
[15] Wen J-J, Zhang R-X: Two conjectured inequalities involving the sums of inscribed polygons in some circles. Journal of Shanxi Normal University 2002, 30(supplement 1):12-17.
[16] Pečarić J, Wen J-J, Wang W-L, Lu T: A generalization of Maclaurin’s inequalities and its applications. Mathematical Inequalities and Applications 2005, 8(4):583-598. · Zbl 1087.26019
[17] Wang B-Y: An Introduction to the Theory of Majorizations. Beijing Normal University Press, Beijing, China; 1990.
[18] Marshall AW, Olkin I: Inequalities: Theory of Majorization and Its Applications, Mathematics in Science and Engineering. Volume 143. Academic Press, New York, NY, USA; 1979:xx+569. · Zbl 0437.26007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.