[PDF] Top 20 The Optimal Convex Combination Bounds of Arithmetic and Harmonic Means for the Seiffert's Mean

... 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

... 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 Q(a, ... 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

... 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

... 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

... 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 bounds ... See full document

... Chu, Y-M, Wang, M-K, Qiu, S-L: Optimal combination bounds of root-square and arithmetic means for Toader mean.. Song, Y-Q, Jiang, W-D, Chu, Y-M, Yan, D-D: Optimal bounds for Toader mean [r] ... 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

... 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

... The authors wish to thank the anonymous referees for their very careful reading of the paper and fruitful comments and suggestions. This research is partly supported by N S Foundation of Hebei Province Grant ... See full document

... Thus ϕ(x) is strictly decreasing on (., ). Considering the fact ϕ(.) = –. . . . < , we have ϕ(x) <  for any x ∈ (., ). In other words, S (x) is strictly decreasing on (., ). Let φ (x) = ... See full document

... the optimal convex combination bounds of the geometric and Neuman means for the Toader-type mean, and give several new upper and lower bounds for the complete elliptic ... See full document

... Optimal bounds for Neuman-Sándor mean in terms of the geometric convex combination of two Seiffert means Hua-Ying Huang, Nan Wang and Bo-Yong Long* *.. Correspondence: [email protected][r] ... 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

... inequalities of this type are well known in the literature, such as L < L(A, G), I(A, G) < I, and T(A, Q) < T ; see, for instance, [, ]. In what follows, we will see that strict con- vexity/concavity of m, ... 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

... Then it is not difficult to verify that f(x) is continuous and strictly increasing in [1/ 2,1]. Note that f(1/2) = A(a,b) <T(a,b) and f(1) = S(a, b) >T(a, b). Therefore, it is nat- ural to ask what are the ... 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

... 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 ...one-parameter harmonic and ... See full document

... Optimal inequalities for bounding Toader mean by arithmetic and quadratic means Tie-Hong Zhao1 , Yu-Ming Chu1* and Wen Zhang2 *.. Correspondence: [email protected] 1 School of Mathem[r] ... See full document