Bounds for the Neuman-Sandor Mean in Terms of the Arithmetic and Contra-Harmonic Means

In this paper, the authors provide several sharp upper and lower bounds for the Neuman-Sandor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyperbolic cosine function.

Automated summary

In this paper, the authors provide sharp upper and lower bounds for the Neuman-Sandor mean and present new inequalities involving hyperbolic sine and cosine functions.