Optimal Convex Combination Bounds of Arithmetic and Second Seiffert Means for Neuman-S´andor Mean

  • Ma Hongyan Hebei University
  • Liu Chunrong Hebei University
Keywords: least value, value β, αA(a, b) (1 − α)T(a, b), M(a, b) < βA(a, b), T(a, b)

Abstract

In this paper, we present the least value α and the greatest value β such that the double inequality αA(a, b) + (1 − α)T(a, b) < M(a, b) < βA(a, b) + (1 − β)T(a, b) hold for all a, b > 0 with a 6= b, where A(a, b), M(a, b) and T(a, b) are the arithmetic, NeumanS´andor and second Seiffert means of a and b, respectively.

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Author Biographies

Ma Hongyan, Hebei University

College of Mathematics and Computer Science, Hebei University, Baoding 071002, P. R. China

Liu Chunrong, Hebei University

College of Mathematics and Computer Science, Hebei University, Baoding 071002, P. R. China

Published
2016-11-30
How to Cite
Hongyan, M., & Chunrong, L. (2016). Optimal Convex Combination Bounds of Arithmetic and Second Seiffert Means for Neuman-S´andor Mean. IJRDO -JOURNAL OF MATHEMATICS, 2(11), 38-44. https://doi.org/10.53555/m.v2i11.1626