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Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

We find the least values p , q , and s in (0, 1/2) such that the inequalities H ( p a + (1 − p ) b , p b + (1 − p ) a ) > AG( a , b ), G ( q a + (1 …