Sentence examples for by the normalized duality from inspiring English sources

Also, we denote by the normalized duality mapping from to defined by (1.1).

Denote by the normalized duality mapping from into defined by (1.1).

We denote by the normalized duality mapping from to defined by (2.1).

We denote by the normalized duality map from E to defined by (1.1).

If, we will denote by the normalized duality mapping at defined by.

Also, we denote by J the normalized duality mapping from E to 2E*defined by.

The value of at is denoted by and the normalized duality mapping from into is defined by (2.1).

We denote by J the normalized duality mapping from E to 2E*defined by J ( x ) = x * ∈ E * : x, x * = x 2 = x * 2, x ∈ E. where 〈·,·〉 denotes the generalized duality pairing.

We denote by J the normalized duality mapping from E to (2^{E^) defined by Jx=bigl{ fin E^:langle x,frangle=|x|^{2}=|f|^{2} bigr}, where (langlecdot,cdotrangle) denotes the generalized duality pairing.

We denote by J the normalized duality mapping from X to 2 X ∗ defined by J x = { x ∗ ∈ X ∗ : 〈 x ∗, x 〉 = ∥ x ∗ ∥ ∥ x ∥, ∥ x ∥ = ∥ x ∗ ∥ }, (2.1).

We denote by J the normalized duality mapping from E to 2 E ∗ defined by J ( x ) = { f ∗ ∈ X ∗ : 〈 x, f ∗ 〉 = ∥ x ∥ 2 = ∥ f ∗ ∥ 2 }.