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TWO DOUBLE INEQUALITIES FOR THE SEIFFERT MEAN IN TERMS OF THE ARITHMETIC, CENTROIDAL, AND CONTRA-HARMONIC MEANS

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In the paper, the authors find the best possible constants such that two double inequalities for bounding the second Seiffert mean in terms of a one-parameter family of the centroidal mean or in terms of a convex combination of the arithmetic and contra-harmonic means are valid.

Abstract

In the paper, the authors find the best possible constants such that two double inequalities for bounding the second Seiffert mean in terms of a one-parameter family of the centroidal mean or in terms of a convex combination of the arithmetic and contra-harmonic means are valid.

참고문헌 (9)

  1. M. Abramowitz, "Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables" (1972)
  2. G. E. Andrews, "Encyclopedia of Mathematics and its Applications" (1999), Cambridge University Press
  3. Y.-M. Chu, "Sharp bounds for Seiffert mean in terms of contraharmonic mean", Abstr. Appl. Anal., 2012, pp.425175~ (2012)[DOI]
  4. Yu-Ming Chu, "Two sharp double inequalities for Seiffert mean", Journal of Inequalities and Applications, 2011(1), pp.44~ (2011), Springer Nature[DOI]
  5. J. Fang, "Some Convex Combination Bounds for Arithmetic and the Second Seiffert Means", Master, pp.2011
  6. P. A. Hästö, "A monotonicity property of ratios of symmetric homogeneous means", J. Inequal. Pure Appl. Math., 3(5), pp.71~ (2002)
  7. "Two sharp inequalities for bounding the Sei ert mean by the arithmetic, centroidal, and contra-harmonic means"[URL]
  8. Wei-dong Jiang, "Some sharp inequalities involving Seiffert and other means and their concise proofs", Mathematical Inequalities & Applications, (4), pp.1007~1017 (1998), Element d.o.o.[DOI]
  9. H.-J. Seiffert, "Aufgabe β 16", Die Wurzel, 29, pp.221~222 (1995)

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