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Applications of the Cauchy-Bouniakowsky inequality in the theory of means

J. Sandor
장전수학회 (Jangjeon Mathematical Society)|2016.04|Advanced Studies in Contemporary Mathematics|제26권 제2호|pp. 237-254

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초록

We o er various inequalities for means, as applications of the classical integral inequality (∫<sup>a<sub>b f(x)g(x)dx)<sup>2 ≤ ((∫<sup>a<sub>b f<sup>2(x)dx) ((∫<sup>a<sub>b g<sup>2(x)dx).

Abstract

We o er various inequalities for means, as applications of the classical integral inequality (∫<sup>a<sub>b f(x)g(x)dx)<sup>2 ≤ ((∫<sup>a<sub>b f<sup>2(x)dx) ((∫<sup>a<sub>b g<sup>2(x)dx).

참고문헌 (16)

  1. V. Bouniakowsky, "Sur quelques inegalites concernant les integrales ordinaires et les integrales aux differences finies, Memoires de l'Academie Imperiale des Sciences de St.-Petersbourg", VIIe serie, Tome I, (9) (1859)
  2. G.H. Hardy, "Inequalities" (1964), Cambridge Univ. Press
  3. E. Neuman, "On the Schwab-Borchardt mean II", Math. Pannonica, 17(1), pp.49~59 (2006)
  4. J. Sandor, "Some integral inequalities", Elem. Math, 43, pp.177~180 (1988)
  5. J. Sandor, "On the identric and logarithmic means", Aequationes Math, 40, pp.261~270 (1990)
  6. J. Sandor, "On some exponential means", Babes-Bolyai Univ. Preprint, 7, pp.35~40 (1990)
  7. J. Sandor, "On certain identities for means", Studia Univ. Babes-Bolyai, Math, 38(4), pp.7~14 (1993)
  8. J. Sandor, "Inequalities for certain means in two arguments", Nieuw Arch. Wiskunde, New Ser, 15(1-2), pp.51~55 (1997)
  9. J. Sandor, "Some general means", Czechoslovak Math. J, 49(124), pp.53~62 (1999)
  10. J. Sandor, "On certain inequalities for means", Arch. Math, 76, pp.34~40 (2001)
  11. J. Sandor, "Some new inequalities for means of two arguments", Int. J. Math. Math. Sci., 25(8), pp.525~532 (2001)
  12. J. Sandor, "On Huygens' inequalities and the theory of means", Intern. J. Math. Math. Sci, 2012, pp.9~ (2012)
  13. J. Sandor, "Bouniakowsky and the logarithmic inequalities, submitted", ~
  14. H.-J. Seiffert, "Werte zwischen dem geometrischen und dem arithmetischen Mittel weier Zahlen", Elem. Math, 42, pp.105~107 (1987)
  15. H.-J. Seiffert, "Problem 887", Nieuw Arch. Wisk, 11, pp.176~ (1993)
  16. H.-J. Seiffert, "Ungleichungen fur einen bestimmten Mittelwert", Nieuw Arch. Wiskunde, 13, pp.195~198 (1995)

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