Sentence examples for preserves gs-majorization from inspiring English sources

Then and hence preserves gs-majorization.

Conversly, if (i) or (iii) holds it is easy to show that preserves gs-majorization.

We use the following statements to find the structure of linear preservers of gs-majorization.

Then linear maps preserving lgw-majorization or gs-majorization and linear maps, preserving rgw-majorization are characterized.

In this paper, the relations gs-majorization, lgw-majorization, and rgw-majorization are considered on and.

Because the exterior derivative d M is linear and commutes with the pullback, it preserves (G, h -invariance under every group G wh -invariance transformations are diffeomorphisms.

The linear map defined by, where, preserves rgw-majorization.

The notaions of generalized majorization (g-majorization) were motivated by the matrix majorization and were introduced in [4 6] as follows.

Linear maps from to that preserve left matrix majorization or weak majorization were already characterized in [10, 11].

A mapping f : X → X is a Banach G-contraction or simply G-contraction if f preserves edges of G; ( x, y ) ∈ E ( G ) ⇒ ( f x, f y ) ∈ E ( G ), (1).

Since f is an order-preserving map, g ( α + 1 ) = f ( g ≤ f ( e ) = e.