Sharp bounds for Sándor mean in terms of arithmetic, geometric and harmonic means

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 bounds for a special quasi-arithmetic mean in terms of arithmetic and geometric means with two parameters

In the article, we present the best possible parameters [Formula: see text] and [Formula: see text] on the interval [Formula: see text] such that the double inequality [Formula: see text] holds for any [Formula: see text] and all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic, geometric and special quasi-ar...

Bounds for the Arithmetic Mean in Terms of the Neuman, Harmonic and Contraharmonic Means

SB (a, b) = { √ b2−a2 cos−1(a/b) , a < b , √ a2−b2 cosh−1(a/b) , a > b . In this paper, we find the greatest values α1, α2, α3 and α4, and the least values β1, β2, β3 and β4 such that the double inequalities α1SAH(a, b) + (1 − α1)C(a, b) < A(a, b) < β1SAH(a, b) + (1 − β1)C(a, b), α2SHA(a, b) + (1 − α2)C(a, b) < A(a, b) < β2SHA(a, b) + (1 − β2)C(a, b), α3SCA(a, b) + (1 − α3)H(a, b) < A(a, b) < β...

Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

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