[PDF] Top 20 Optimal bounds for arithmetic geometric and Toader means in terms of generalized logarithmic mean

... 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

... B.-Y.: Optimal bounds for Neuman–Sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic ...M.-K.: Optimal Lehmer mean ... See full document

... for generalized logarithmic, arithmetic, and geometric means,” Journal of Inequalities and Applications, ...for means in two variables,” Archiv der Mathematik, ... See full document

... Schwab-Borchardt mean SB(a, b) is strictly increasing in both a and b, nonsymmetric and homogeneous of degree ...ate means are special cases of the Schwab-Borchardt ...Seiffert mean, T (a, b) = (a – ... See full document

... 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 ...new ... 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

... the logarithmic mean has been : the subject of intensive ...the logarithmic mean can be found in the literature ...the logarithmic mean has applications in physics, economics, ... 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

... B-Y: Optimal bounds for Neuman-Sándor mean in terms of the convex combinations of harmonic, geometric, quadratic, and contraharmonic ...some means derived from the ... 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

... Chen, “The monotonicity of the ratio between generalized logarithmic means,” Journal of Mathematical Analysis and Applications, vol.. Qi, “Monotonicity result for generalized logarithmic[r] ... See full document

... We also give an improved upper bound of the logarithmic mean on Theorem . above, only for the Frobenius norm. Namely, we can prove the following inequalities in a similar way to the proof of Theorem ., ... 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

... k ∈ 0, ∞ for fixed a, b > 0 with a / b. Let Aa, b a b/2, Ia, b 1/eb b /a a 1/b−a , La, b b − a/log b − log a, Ga, b √ ab, and Ha, b 2ab/a b be the arithmetic, identric, logarithmic, geometric, and ... See full document

... the optimal upper and lower bounds for the Neuman-Sándor mean M(a, b) in terms of the geometric convex combinations of the first Seiffert mean P(a, b) and the quadratic mean ... See full document

... standard means was presented in []. For example, the arithmetic, geometric, and harmonic means A, G, and H are ...The logarithmic mean L is (H, A)-stabilizable and (A, ... See full document

... The invariance of the arithmetic mean with respect to various quasi-arithmetic means has been extensively investigated. Firstly we came upon the work of Sutô [5] [6] presented in 1914, in ... See full document

... Liu, Optimal bounds for Neuman-S´aandor mean in terms of the con- vex combinations of harmonic, geometric, quadratic, and contraharmonic means, Abstr. Jiang and Y.-M[r] ... 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

... 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