Arithmetic, geometric, harmonic, and quadratic means

Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means

A Note on the Weighted Harmonic–geometric–arithmetic Means Inequalities

In this note, we derive non trivial sharp bounds related to the weighted harmonicgeometric-arithmetic means inequalities, when two out of the three terms are known. As application, we give an explicit bound for the trace of the inverse of a symmetric positive definite matrix and an inequality related to the coefficients of polynomials with positive roots. Mathematics subject classification (201...

Optimal bounds for Neuman means in terms of geometric, arithmetic and quadratic means

*Correspondence: [email protected] 2School of Mathematics and Computation Science, Hunan City University, Yiyang, 413000, China Full list of author information is available at the end of the article Abstract In this paper, we present sharp bounds for the two Neuman means SHA and SCA derived from the Schwab-Borchardt mean in terms of convex combinations of either the weighted arithmetic and ...

A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions

and Applied Analysis 3 called cofinite if the recession function f0 of f satisfies f0 y ∞, for all y / 0 see 15, page 116 . Then f is cofinite if and only if dom f∗ R by means of 15, Corollary 13.3.1 . The terminology “cofinite” is renewed as “coercive” in 16, 3.26 Theorem . Now we take a look at Atteia and Raı̈ssouli 11, Proposition 4.4 with a refined proof. Proposition 2.1 See Atteia and Raı̈ss...

Comparison of Harmonic, Geometric and Arithmetic means for change detection in SAR time series

The amplitude distribution in a SAR image can present a heavy tail. Indeed, very high–valued outliers can be observed. In this paper, we propose the usage of the Harmonic, Geometric and Arithmetic temporal means for amplitude statistical studies along time. In general, the arithmetic mean is used to compute the mean amplitude of time series. In this study, we will show that comparing the behavi...