Optimal Bounds for Neuman-S´andor Mean in Terms of the Convex Combination of Geometric and Contra-harmonic Means

  • He Haibin Hebei University
  • Liu Chunrong Hebei University,
DOI: https://doi.org/10.53555/m.v2i11.1623
Keywords: least value, value β, inequality, M(a, b), βG(a, b)

Abstract

In this paper, we present the least value α and the greatest value β such that the double inequality αG(a, b) + (1 − α)C(a, b) < M(a, b) < βG(a, b) + (1 − β)C(a, b) holds for all a, b > 0 with a 6= b, where G(a,b), M(a,b) and C(a,b) are respectively the geometric, Neuman-S´andor and contra-harmonic means of a and b.

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Author Biographies

He Haibin, Hebei University

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

Liu Chunrong, Hebei University,

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

Published
2016-11-30
How to Cite
Haibin, H., & Chunrong, L. (2016). Optimal Bounds for Neuman-S´andor Mean in Terms of the Convex Combination of Geometric and Contra-harmonic Means. IJRDO -JOURNAL OF MATHEMATICS, 2(11), 27-37. https://doi.org/10.53555/m.v2i11.1623
Issue
Vol. 2 No. 11 (2016): IJRDO-Journal of Mathematics
Section
Articles

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