Sentence examples for maps the ball from inspiring English sources

that is maps the ball to itself.

So we obtain this result: N maps the ball (B_{r}) of radius r into itself.

Therefore, N maps the ball of B R of radius R into itself, when T satisfies (3.1).

end{aligned}Consequently, the operator (tau) maps the ball (B_{r_{0}}subset C[0,1]) into itself.

Thus, in view of Definition 2.1, the operator U maps the ball (A_{gamma_{0}}) into its own subset (S rho_{1}, eta)).

Proof We show that there exists n ∈ N such that the operator T n maps the ball Q n into itself.

Inspired by earlier work of the French mathematician Henri Poincaré, Brouwer investigated the behaviour of continuous functions (see continuity) mapping the ball of unit radius in n-dimensional Euclidean space into itself.

This implies that S and K map the ball B r into B r, where r = 1 1 − b B ( 1 − e − 1 ) with b < B e e − 1.

We find that up to normalization, an NC ball map is the direct sum of the identity map with an NC analytic map of the ball into the ball.

Then the nonlinear mapping T defined above has a unique fixed point v in B. Proof The previous lemma shows that, if τ is chosen small enough, the nonlinear mapping T is a contraction mapping from the ball B of radius 2 c κ τ 5 / 2 in C δ 2, α ( M k, τ ) into itself.

Hence, (|u xi |le R), and T maps the closed ball (B:={vin H |v|le R}) into itself.