Sentence examples for be a normed vector from inspiring English sources

Let X be a normed vector spacewith norm ∥ · ∥.

Open image in new window This implies that the inequality (Equation 2. □. Let θ ≥ 0 and let r be a real numberwith r > 1. Let X be a normed vector spacewith norm ∥ · ∥. Let f :X → Y be an odd mapping, satisfyingEquation 14, and then A ( x ) : = N - lim n → ∞ 2 n f x 2 n − 1 − 8 f x 2 n Open image in new window.

In this section, let be a normed vector space with norm a Banach space with norm and an even integer.

Let be a normed vector space with norm.

Let X be a normed vector space with norm ∥·∥.

Let be a normed vector space with norm || · || Let f : X → Y be a mapping satisfying (2.11), (2.12), and (2.13).

If (( X, Vert ; Vert )) is a normed vector space then there is always a metric-induced norm (d ( x, y ) = Vert x - y Vert ), (forall x, y in X).

Throughout this section, X is a normed vector space and Y is a Banach space.

Throughout this paper, assume that X is a normed vector space and that ( Y, ∥ ⋅ ∥ ) is a Banach space.

If S is a normed vector space and there is a nontrivial stability couple (i.e. φ ≠ 0 ) such that the control function φ is defined with the help of the norm from S, we say that the equation is stable in the Aoki-Rassias sense (see [17] and [18] for the origin of the eponymies).

The last equality in (3.4) arises for any given (a, b in X), since (( X, Vert ; Vert )) is a normed vector space, one has trivially (Vert a + b - a Vert = Vert b Vert ) and, since (0 in X), it follows that (F_{a + b, a} ( t ) = F_{b, 0} ( t )), (forall t in mathbf{R}_), in the Menger PM space (( X,F,Delta_{M} )).