We find the least values , , and in (0, 1/2) such that the inequalities , , , and hold for all with , respectively. Here , and denote the arithmetic-geometric, harmonic, geometric, and logarithmic means of two positive numbers a and b, respectively.
J. Appl. Math.
2011:
1-9
(2011).
DOI: 10.1155/2011/618929