Improved logarithmic-geometric mean inequality and its application

Improved Heinz inequality and its application

* Correspondence: limin-zou@163. com School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404100, People’s Republic of China Abstract We obtain an improved Heinz inequality for scalars and we use it to establish an inequality for the Hilbert-Schmidt norm of matrices, which is a refinement of a result due to Kittaneh. Mathematical Subject Classification 2010: 26D07;...

The matrix arithmetic-geometric mean inequality revisited

Improved mean estimation and its application to diagonal discriminant analysis

MOTIVATION High-dimensional data such as microarrays have created new challenges to traditional statistical methods. One such example is on class prediction with high-dimension, low-sample size data. Due to the small sample size, the sample mean estimates are usually unreliable. As a consequence, the performance of the class prediction methods using the sample mean may also be unsatisfactory. T...

A Weighted Geometric Inequality and Its Applications

A new weighted geometric inequality is established by Klamkin’s polar moment of inertia inequality and the inversion transformation, some interesting applications of this result are given, and some conjectures which verified by computer are also mentioned

A Relationship between Subpermanents and the Arithmetic-Geometric Mean Inequality

Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n × n matrices F. In the case k = n, we exhibit an n 2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries.

Sharp Two Parameter Bounds for the Logarithmic Mean and the Arithmetic–geometric Mean of Gauss

For fixed s 1 and t1,t2 ∈ (0,1/2) we prove that the inequalities G(t1a + (1− t1)b,t1b+(1− t1)a)A1−s(a,b) > AG(a,b) and G(t2a+(1− t2)b,t2b+(1− t2)a)A1−s(a,b) > L(a,b) hold for all a,b > 0 with a = b if and only if t1 1/2− √ 2s/(4s) and t2 1/2− √ 6s/(6s) . Here G(a,b) , L(a,b) , A(a,b) and AG(a,b) are the geometric, logarithmic, arithmetic and arithmetic-geometric means of a and b , respectively....