A unified proof of several inequalities and some new inequalities involving Neuman-S\'andor mean

In the paper, by finding linear relations of differences between some means, the authors supply a unified proof of some double inequalities for bounding Neuman-Sandor means in terms of the arithmetic, harmonic, and contra-harmonic means and discover some new sharp inequalities involving Neuman-Sandor, contra-harmonic, root-square, and other means of two positive real numbers.