IJPAM: Volume 92, No. 4 (2014)
THE CONTRAHARMONIC AND HARMONIC MEANS
FOR THE WEIGHTED GEOMETRIC MEAN
College of Mathematics and Computer Sciences
Baoding, 071002, P.R. CHINA
Abstract. We find the greatest value and the least value such that the double inequality
holds for all with . Here , and denote the contraharmonic, harmonic, and the weighted geometric means of two positive numbers and respectively.
Received: January 26, 2014
AMS Subject Classification: 65N15
Key Words and Phrases: optimal convex combination bound, contraharmonic mean, harmonic mean, the weighted geometric mean
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DOI: 10.12732/ijpam.v92i4.15 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 599 - 607
This work is licensed under the Creative Commons Attribution International License (CC BY).