Sharp Geometric Mean Bounds for Neuman Means

Optimal convex combination bounds of geometric and Neuman means for Toader-type mean

In this paper, we prove that the double inequalities [Formula: see text] hold for all [Formula: see text] with [Formula: see text] if and only if [Formula: see text], [Formula: see text] , [Formula: see text] and [Formula: see text] , where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text] are the Toader, geometric, arithmetic and two Neu...

Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means

Optimal bounds for Neuman means in terms of geometric, arithmetic and quadratic means

*Correspondence: [email protected] 2School of Mathematics and Computation Science, Hunan City University, Yiyang, 413000, China Full list of author information is available at the end of the article Abstract In this paper, we present sharp bounds for the two Neuman means SHA and SCA derived from the Schwab-Borchardt mean in terms of convex combinations of either the weighted arithmetic and ...

Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means

and Applied Analysis 3 The following sharp lower power mean bounds for 1/3 G a, b 2/3 H a, b , 2/3 G a, b 1/3 H a, b , and P a, b can be found in 4, 6 : 1 3 G a, b 2 3 H a, b > M−2/3 a, b , 2 3 G a, b 1 3 H a, b > M−1/3 a, b , P a, b > Mlog 2/ logπ a, b 1.8 for all a, b > 0 with a/ b. The purpose of this paper is to answer the question: for α ∈ 0, 1 , what are the greatest value p and the least...

Sharp Bounds for Seiffert Mean in Terms of Weighted Power Means of Arithmetic Mean and Geometric Mean

For a,b > 0 with a = b , let P = (a− b)/(4arctana/b−π) , A = (a+ b)/2 , G = √ ab denote the Seiffert mean, arithmetic mean, geometric mean of a and b , respectively. In this paper, we present new sharp bounds for Seiffert P in terms of weighted power means of arithmetic mean A and geometric mean G : ( 2 3 A p1 + 3 G p1 )1/p1 < P < ( 2 3 A p2 + 3 G p2 )1/p2 , where p1 = 4/5 and p2 = logπ/2 (3/2)...