Sharp bounds for Seiffert means in terms of Lehmer means

Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

and Applied Analysis 3 2. Proof of Theorem 1.1 Proof of Theorem 1.1. Let λ 1 √ 4/π − 1 /2 and μ 3 √3 /6. We first proof that the inequalities T a, b > C λa 1 − λ b, λb 1 − λ a , 2.1 T a, b < C ( μa ( 1 − μb, μb 1 − μa 2.2 hold for all a, b > 0 with a/ b. From 1.1 and 1.2 we clearly see that both T a, b and C a, b are symmetric and homogenous of degree 1. Without loss of generality, we assume th...

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)...

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...

Optimal Bounds for Seiffert Mean in terms of One-Parameter Means

Optimal bounds for Neuman-Sándor mean in terms of the convex combination of the logarithmic and the second Seiffert means

In the article, we prove that the double inequality [Formula: see text] holds for [Formula: see text] with [Formula: see text] if and only if [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] denote the Neuman-Sándor, logarithmic and second Seiffert means of two positive numbers a and b, respectively.