Sentence examples for coercive function from inspiring English sources

This power is not available for anyone to use: Aquinas argues that the coercive function should be "vested in the whole people or in some public personage," and not allowed to private parties (Aquinas, ST, I.II Q90 A3).

Let K be a nonempty closed convex subset of a reflexive Banach space E. Assume that (varphi Kto R) is a proper convex lower semi-continuous and coercive function.

Here A = { x ∈ D : t x + = + ∞ } is the basin of attraction of x 0. In 1992, using the nonnegative auxiliary scalar coercive function, that is, continuous mappings k : E → R + with k ( x ) → + ∞ as ∥ x ∥ → + ∞, Zampieri [9] also generalized the Hadamard-Levy theorem to show the following situation.

Then dom ( T r ) = E. Lemma 5.2 Let E be a reflexive Banach space and let g : E → R be a convex, continuous and strongly coercive function which is bounded on bounded subsets and uniformly convex on bounded subsets of E. Let C be a nonempty, closed and convex subset of E and let f : C × C → R be a bifunction satisfying (A1 - A4).

Let E be a reflexive Banach space and let (f : E rightarrow R) be a convex, continuous, and strongly coercive function which is bounded on bounded subsets and uniformly convex on bounded subsets of E. Let C be a nonempty, closed, and convex subset of E and let (F : C times C rightarrow R) be a bifunction satisfying (A1 - A4).

The mapping f ∈ C 1 ( E ; F ) is a global diffeomorphism onto F if (1) f ′ ( x ) ∈ Isom ( E, F ) ∀ x ∈ E ;   (2) sup ∥ x ∥ ≤ r ∥ f ′ ( x ) − 1 ∥ < + ∞ ∀ r : 0 < r < + ∞ ;   (3) there exists a locally Lipschitzian coercive function k : E → R + which admits all D V + k ( x ), and it is such that sup { D V + k ( x ) : v = f ′ ( x ) − 1 u, x ∈ E, u ∈ F, ∥ u ∥ = 1 } < + ∞.  .

Thus, the party, in effect, assumes the coercive functions of the state during the dictatorship of the proletariat or, to be more accurate, during the dictatorship of the party in the name of the proletariat.

In [20], the authors discussed the case that (1< q< p< q^), (p< N) with h, g continuous, positive, and coercive functions on (mathbb{R}^{N}) and (f x,s)) a Carathéodory function satisfying some conditions.

The Euclidean projector (P_{K}) and (I-P_{K}) are both 'co-coercive' functions [2, 19].

Let E be a reflexive Banach space, (g:Etomathbb{R}) be a strongly coercive Bregman function and V be the function defined by V_{g}bigl x,x^bigr)=g(x -bigllangle x -bigllanglele +g^ bigl(x^bigr),x^ad xin E, x^in E^.

Lemma 2.5 Let E be a reflexive Banach space, let g : E → R be a strongly coercive Bregman function and let V be the function defined by V ( x, x ∗ ) = g ( x ) − 〈 x, x ∗ 〉 + g ∗ ( x ∗ ), x ∈ E, x ∗ ∈ E ∗.