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

Abstract

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

Keywords

• Neuman–Sándor mean
• arithmetic mean
• contra-harmonic mean
• bound
• inequality
• hyperbolic sine function