Sentence examples for for any exists from inspiring English sources

Let be a sequence in defined by (1.12), then we have, for any, exists.

Since each is compact, by for any, exists for all and all.

We define that is continuous for any ; and exist and, is continuously differentiable for any ;, exist and.

In order to define the concept of solution for (1), we introduce the following spaces of functions: is continuous for any,, exist, and, is continuously differentiable for any,, exist, and.

Cases 1 5 show that for any, there exists, for any there exists such that for.

Then is called almost -convex if, for any and for any, there exists a mapping such that for all and.

Hence, (i), for any ; (ii)for any, there exists such that.

and -nonexpansive-type if for any and for any, there exists such that (2.2).

For, by, for any, there exists such that for all, (2.20).

Then, and for all, for any, there exists a point such that for all.

One calls that is almost periodic, if for any, there exists such that for any, there exists such that (2.13).