[PDF] Top 20 Sharp bounds for the arithmetic geometric mean

... Abstract In this article, we establish some new inequality chains for the ratio of certain bivariate means, and we present several sharp bounds for the arithmetic-geometric mean.. MSC: P[r] ... See full document

... Yang, Z.-H., Qian, W.-M., Chu, Y.-M., Zhang, W.: On approximating the arithmetic–geometric mean and complete elliptic integral of the first kind.. Lin, L., Liu, Z.-Y.: An alternating proj[r] ... See full document

... 5 Conclusion We present sharp upper and lower bounds for the Sándor–Yang means RAQ and RQA in terms of the arithmetic and contraharmonic means and provide new bounds for the Seiffert mea[r] ... See full document

... Wu, “Generalization and sharpness of the power means inequality and their applications,” Journal of Mathematical Analysis and Applications, vol.. Richards, “Sharp power mean bounds for t[r] ... See full document

... Correspondence: [email protected] 2 School of Mathematics and Computation Sciences, Hunan City University, Yiyang, 413000, China Full list of author information is available at the e[r] ... See full document

... the arithmetic mean A(a, b) [1–4], the quadratic mean Q(a, b) [5], the contra-harmonic mean C(a, b) [6–9], the Neuman–Sándor mean NS(a, b) [10–12], the second Seiffert mean T (a, ... See full document

... Wu, “Generalization and sharpness of the power means inequality and their applications,” Journal of Mathematical Analysis and Applications, vol.. Richards, “Sharp power mean bounds for t[r] ... See full document

... Optimal bounds for Neuman-Sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic ...Optimal bounds for Neuman means in terms of harmonic and ... See full document

... Chu, Y-M, Zong, C, Wang, G-D: Optimal convex combination bounds of Seiffert and geometric means for the arithmetic mean.. Borwein, JM, Borwein, PB: Inequalities for compound mean iteratio[r] ... See full document

... Î ℝ for fixed a, b >0 with a ≠ b. Let A(a, b) = (a + b)/2, G(a, b) = √ ab , H(a, b) = 2ab/(a + b), I(a, b) = 1/e(b b /a a ) 1/(b-a) (b ≠ a), I(a, b) = a (b = a), and L(a, b) = (b-a)/ (log b-log a) (b ≠ a), L(a, b) = a ... See full document

... Optimal bounds for arithmetic-geometric and Toader means in terms of generalized logarithmic mean Qing Ding1 and Tiehong Zhao2* *.. Correspondence: [email protected] 2 Department [r] ... See full document

... Matejíčka, L: Sharp bounds for the weighted geometric mean of the first Seiffert and logarithmic means in terms of weighted generalized Heronian mean.. Yang, Z-H: Sharp bounds for Seiffert[r] ... See full document

... Schwab-Borchardt mean SB(a, b) is strictly increasing in both a and b, nonsymmetric and homogeneous of degree ...Seiffert mean, T (a, b) = (a – b)/[ arctan((a– b)/(a +b))] = SB[A(a, b), Q(a, b)] is the ... See full document

... the sharp bounds for the Sándor–Yang mean in terms of certain families of the two-parameter geometric and arithmetic mean and the one-parameter geometric and harmonic ... See full document

... the sharp bounds for the special quasi-arithmetic mean E(a, b) in terms of the arithmetic mean A(a, b) and geometric mean G(a, b) with two ...and geometric ... See full document

... b=0,geometric mean and harmonic mean will be ...the arithmetic mean derivative - based closed Newton-Cotes quadrature rule gives better solution than the other ... See full document

... curvature bounds and their measured Gromov Hausdorff limits (for the theory of Ricci limit spaces, see Cheeger and Colding [20; 21; 22; 23] and Colding and Naber [24]), Alexandrov spaces satisfying lower curvature ... See full document

... two-variable geometric mean has sprung up for positive operators: For two positive operators A and B, the operator geometric mean is defined by AB := A 1 2 (A – 1 2 BA – 2 1 ) 1 2 A 1 2 for A ... See full document

... We find the greatest value α and least value β such that the double inequality αAa, b 1 − αHa, b < P a, b < βAa, b1−βHa, b holds for all a, b > 0 with a / b. Here Aa, b, Ha, b, and Pa, b denote the ... See full document

... We present in this paper a necessary and sufficient condition to establish the inequality between generalized weighted means which share the same sequence of numbers but differ in the weights. We first present a sufficient ... See full document