
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.
contra-harmonic mean, bound, inequality, hyperbolic sine function, QA1-939, Neuman–Sándor mean, Neuman–Sándor mean; arithmetic mean; contra-harmonic mean; bound; inequality; hyperbolic sine function; hyperbolic cosine function, Mathematics, arithmetic mean
contra-harmonic mean, bound, inequality, hyperbolic sine function, QA1-939, Neuman–Sándor mean, Neuman–Sándor mean; arithmetic mean; contra-harmonic mean; bound; inequality; hyperbolic sine function; hyperbolic cosine function, Mathematics, arithmetic mean
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