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Majorized proof of arithmetic-geometric-harmonic means inequality

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초록

As we all know, arithmetic -geometric mean inequalities are the most basic and important inequalities. To seek different method to prove them has been one of the study focuses and they have been proven by more than a hundred ways By using methods based on the theory of majorization, the arithmetic-geometric-harmonic means inequality is proved in a new way.

Abstract

As we all know, arithmetic -geometric mean inequalities are the most basic and important inequalities. To seek different method to prove them has been one of the study focuses and they have been proven by more than a hundred ways By using methods based on the theory of majorization, the arithmetic-geometric-harmonic means inequality is proved in a new way.

참고문헌 (13)

  1. A. M. Marshall, "Inequalities:theory of majorization and its application" (1979), Academies Press
  2. B.-Y. Wang, "Foundations of Majorization Inequalities" (1990), Beijing Normal Univ. Press
  3. X.-M. Zhang, "Geometrically Convex Functions" (2004), An’hui University Press
  4. C. P. Niculescu, "Convexity According to the Geometric Mean", Mathematical Inequalities &Applications, 3(2), pp.155~167 (2000)
  5. P.S. Bullen, "Means and their inequalities" (1988), Reidel publishing Co.
  6. J.-C. Kuang, "Applied Inequalities (Chang yong bu deng shi)" (2010), Shandong Press of Science and Technology
  7. Yasuharu Uchida, "Geometric-arithmetic mean inequality", J. Inequal. Pure and Appl. Math, 9(2) (2008)
  8. Josip Pˇecari´c, "A new proof of the arithmetic mean-the geometric mean inequality", J. Math. Anal. Appl, 215, pp.577~578 (1997)
  9. Hao Zhi Chuan, "Note on the inequality of the arithmetic and geometric means", Pacific Journal Of Mathematics, 143(1), pp.43~46 (1990)
  10. Chung Lie Wang, "A generalization of the HGA inequalities", Soochow J. Math. Natur. Sci, 6, pp.149~152 (1980)
  11. Hansheng Yang, "The arithmetic-geometric mean inequality and the constant e", Mathematics Magazine, 74(4), pp.321~323 (2001)
  12. Wan-lan Wang, "Some Inequalities Involving Means and Their Converses", J. Math. Anal. Appl., 238(2), pp.567~579 (1999)
  13. Chung-Lie Wang, "Convexity and inequalities", J. Math. Anal. Appl, 72(1), pp.355~361 (1979)

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