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Published in last 50 years
We find the greatest value and least value such that the double inequality holds for all with . Here , , and denote the arithmetic, harmonic, and Seiffert's means of two positive numbers and , respectively.
For , the power-type Heron mean and the Seiffert mean of two positive real numbers and are defined by , ; , and , ; , , respectively. In this paper, we find the greatest value and the least value such that the double inequality holds for all with .
In this paper optimal inequalities between Seiffert’s mean and power means are derived using a simple monotony property. Mathematics subject classification (2000): 26E60, 26D05.