Sentence examples for exists continuous from inspiring English sources

Since, are uniformly bounded and equicontinuous, there exists continuous function, and a subsequence of (denote it again by ), such that,  uniformly in.

By the given conditions of Theorems 2.11 and 2.5, we know that there exists continuous implicit function determined by parametric variational inequality with respect to in SVI.

By Corollary 2.9, there exists continuous implicit function determined by parametric variational inequality with respect to in SVI such that for all, is the unique solution to.

Let the following condition be fulfilled: (H) There exists continuous function such that ∥ V ( t, s ) ξ ∥ ≤ k ( t, s ) ∥ ξ ∥, where 0 ≤ s < t and ξ ∈ D ( A ( s ) ).

A subset of is said to be a retract if there exists continuous mapping such that, for all, and every closed convex subset of a uniformly convex Banach space is a retract.

In fact, we can find a continuous function ϕ ( t, v ) such that f v v ( t, v ) + ϕ v v ( t, v ) ≥ 0, where ϕ v v ( t, v ) exists, continuous with ϕ v v ( t, v ) ≥ 0. In a similar manner, the convexity assumption on K ( t, s, v ) and the concavity assumption on g ( u ) can be relaxed.

There exist continuous and nondecreasing such that.

Also assume that there exist continuous functions such that (3.33).

(H2 There exist continuous, nonnegative functions and such that.

(H5 there exist continuous nonnegative functions such that (4.3). is nonincreasing and is nondecreasing in.

Suppose that is differential, and there exist continuous functions for and a constant such that for.