Refinements of Bounds for Neuman Means

Yu-Ming Chu; Wei-Mao Qian

doi:10.1155/2014/354132

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Home > Journals > Abstr. Appl. Anal. > Volume 2014 > Article

2014 Refinements of Bounds for Neuman Means

Yu-Ming Chu, Wei-Mao Qian

Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/354132

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Abstract

We present the sharp bounds for the Neuman means ${S}_{HA}$ , ${S}_{AH}$ , ${S}_{CA}$ and ${S}_{AC}$ in terms of the arithmetic, harmonic, and contraharmonic means. Our results are the refinements or improvements of the results given by Neuman.