Sentence examples for a continuous function from from inspiring English sources

Then, is a continuous function from to, and (3.18).

Here f is a continuous function from ℝ into ℝ.

If (i - iii) are sati - iii u is areosatisfiedhere equal to a contisuous function from [ almost into X.

and g ( y ) : = μ n d ( x n, y ) 2. defines a continuous function from C into ℝ.

Let X be a nonempty, convex, bounded, and closed subset of (mathbb{R}^{n}), and φ be a continuous function from X to itself.

Since any non-Archimedean norm satisfies the triangle inequality, any non-Archimedean norm is a continuous function from its domain to real numbers.

Define a continuous function f from C into [ 0, ∞ ) by f ( x ) = lim sup n → ∞ η ( ∥ T n u − x ∥ ) (9). for all x ∈ C. Then f is well defined from the assumption.

(a: Omegatimesmathbb{R}timesmathbb{R}^{N}rightarrow mathbb{R}^{N}) is a Carathéodory vector function satisfying: there exists a continuous function α from (mathbb{R}_) into (mathbb {R}_) such that (alpha(0)=0) and (alpha(s)>0) if (s>0) and begin{aligned}& a x,xi xigeqalphabigl vertrt svert bigr)|xi|^{p},quad forall sin R, mbox{a.e.e

(H1):  (a: Omegatimesmathbb{R}timesmathbb{R}^{N}rightarrow mathbb{R}^{N}) is a Carathéodory vector function satisfying: there exists a continuous function α from (mathbb{R}_) into (mathbb {R}_) such that (alpha(0)=0) and (alpha(s)>0) if (s>0) and begin{aligned}& a x,xi xigeqalphabigl vertrt svert bigr)|xi|^{p},quad forall sin R, mbox{a.e.e

} (x,t in Q, forall sinmathbb{R} mbox{ and } forallxiinmathbb{R}^{N}. (H2):  There exist a continuous function b from (mathbb {R}^) into (mathbb{R}^) and a nonnegative function (cin L^{p' x,t)}(Q)) such that bigl|a x,t,xi bigr|leqeq bbigl(|s|bigr) bigl[|xi|^{p x,t -1}+c x,t -1}+c x quad mbox{a.e.

Furthermore, we assume that there exists a continuous function α from (mathbb{R}^) into (mathbb{R}^) such that (alpha(0)=0) and (a x,xi xigeqalphaha(|s|)|xi|^{p}) for any (sinmathbb{R}), (xi in mathbb{R}^{N}), and almost every x in Ω.