Sentence examples for mean inequality for from inspiring English sources

In this section, we will discuss the reverse Heinz mean inequality for unitarily invariant norms.

which follows from the the arithmetic-geometric mean inequality for operators (see [15]).

Inequality (1.5) yields the well-known arithmetic-geometric mean inequality for singular values as special cases.

The following three theorems are our main reverse forms of the μ-weighted arithmetic-harmonic mean inequality for scalars.

Sagae and Tanabe [6] establish a mixed A-G mean inequality for a finite number of strictly positive operators.

In Section 3, utilizing the refined Young inequality and iteration method, we establish some weighted arithmetic-geometric mean inequality for two positive operators.

Firstly, the direct reverse weighted arithmetic-harmonic mean inequalities for scalars are obtained.

Some related arithmetic-geometric mean and Heinz mean inequalities for a generalized singular number of τ-measurable operators are proved.

In such a way, they get refinements and converses of numerous mean inequalities for Hilbert space operators.

By using the extreme points theory we obtain necessary and sufficient convolution conditions, coefficients estimates, distortion theorems, and integral mean inequalities for these classes of functions.

The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for the classes of functions with varying argument of coefficients.