Optimal inequalities among various means of two arguments. (English) Zbl 1187.26017

Shi, Ming-Yu; Chu, Yu-Ming; Jiang, Yue-Ping

Abstr. Appl. Anal. 2009, Article ID 694394, 10 p. (2009).

Summary: We establish two optimal inequalities among power mean \(M_p(a,b)= (a^p/2+ b^p/2)^{1/p}\), arithmetic mean \(A(a,b)= (a+b)/2\), logarithmic mean \(L(a,b)= (a-b)/(\log a-\log b)\), and geometric mean \(G(a,b)= \sqrt{ab}\).

MSC:

26E60

Means

References:

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