Sentence examples for be a generalized duality from inspiring English sources

Let E be a Banach space and (J_{q}) be a generalized duality mapping.

For q > 1,a mapping J q : X → 2 X ∗ is said to be a generalized duality mapping if it is defined by J q ( x ) = { f ∗ ∈ X ∗ : 〈 x, f ∗ 〉 = ∥ x ∥ q, ∥ f ∗ ∥ = ∥ x ∥ q − 1 }, ∀ x ∈ X.

Definition 2.1 An operator T : C → E is said to be μ-Lipschitz continuous in the first variable if there exists a constant μ > 0 such that ∥ T ( x, ⋅ ) − T ( y, ⋅ ) ∥ ≤ μ ∥ x − y ∥, ∀ x, y ∈ C. Definition 2.2 Let C be a nonempty closed convex subset of a smooth Banach space E, and J q : E → E ∗ is a generalized duality mapping.

It's a generalized term.

And one is a generalized conspiracy count.

There's a generalized resistance to higher taxes.

There is a generalized form as well.

In reality, "religion" is a generalized term.

Respondents reported this was a generalized phenomenon.

Let (j_{p}: Xrightarrow X^{ast}) be the generalized duality mapping and let (T: Crightarrow X^{ast}) be a bounded Lipschitz continuous nonlinear mapping.

Let E be a real Banach space, and let J q : E → 2 E ∗ be the generalized duality mapping.