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BOUNDS FOR THE QUOTIENTS OF DIFFERENCES OF CERTAIN BIVARIATE MEANS

Jozsef Sandor|EDWARD NEUMAN
장전수학회 (Jangjeon Mathematical Society)|2013.01|Advanced Studies in Contemporary Mathematics|제23권 제1호|pp. 59-66

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참고문헌

키워드

Schwab-Borchardt meanlemniscatic meanlog-arithmic meanSeiffert meansinequalities.
주제분류수학

초록

Bounds for the quotients of differences involving the Schwab-Borchardt mean and the lemniscatic mean are obtained. Inequalities involving means such as logarithmic mean, two Seiffert means and other means are also derived.

Abstract

Bounds for the quotients of differences involving the Schwab-Borchardt mean and the lemniscatic mean are obtained. Inequalities involving means such as logarithmic mean, two Seiffert means and other means are also derived.

참고문헌 (10)

  1. J.M. Borwein, "Pi and AGM: A Study in Analytic Number Theory and Computational Complexity" (1987), John Wiley and Sons
  2. B.C. Carlson, "Algorithms involving arithmetic and geometric means", Amer. Math. Monthly, 78, pp.496~505 (1971)
  3. B.C. Carlson, "The logarithmic mean", Amer. Math. Monthly, 79, pp.615~618 (1972)
  4. E. Neuman, "On Gauss lemniscate functions and lemniscatic mean", Math. Pannon, 18, pp.77~94 (2007)
  5. E. Neuman, "Inequalities involving inverse circular and inverse hyperbolic functions II", J. Math. Inequal, 4, pp.11~14 (2010)
  6. E. Neuman, "On the Schwab-Borchardt mean", Math. Pannon, 14, pp.253~266 (2003)
  7. J. Sandor, "On certain inequalities for means III", Arch. Math. (Basel), 76, pp.34~40 (2001)
  8. J. Sandor, "Uber zwei Mittel von Seiffert", Wurzel, 36, pp.104~107 (2002)
  9. H.-J. Seiffert, "Problem 887", Nieuw. Arch. Wisk, 11, pp.176~ (1993)
  10. H.-J. Seiffert, "Aufgabe 16", Wurzel, 29, pp.87~ (1995)

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