Sentence examples for bounded function such that from inspiring English sources

where is a bounded function such that (3.4).

We introduce a small parameter ε, which will tend to zero, and h a smooth bounded function such that (0< h_{star}leq h ( x^{prime} ) leq h^{star}), for all (( x^{prime},0 ) inomega).

(5) The one-parameter family of mappings from into itself is called a demicontractive semigroup if for all and the conditions (a)–(c) and the following condition (h) are satisfied:   (h) there exists a bounded function such that, for any, and, there exists such that (1.7)  .

The one-parameter family of mappings from into itself is called a strictly pseudocontractive semigroup if the conditions (a)–(c) and the following condition (g) are satisfied: there exists a bounded function such that, for any given, there exists such that (1.6).

If ({c: mathbb{R}^ rightarrow mathbb{R}^) be a right locally bounded from above and (H: mathbb{R}^times mathbb{R}^ rightarrow mathbb{R}^) be a locally bounded function such that, for all (xin X), d x,Tx leq H bigl(c bigl phi(x) bigr),c bigl phi(Tx) bigr) bigr) bigl[ phi(x -phi(Tx -phir].

(4) The one-parameter family of mappings from into itself is called a strictly pseudocontractive semigroup if the conditions (a)–(c) and the following condition (g) are satisfied:   (g) there exists a bounded function such that, for any given, there exists such that (1.6)  .

There exist a continuous function and a locally bounded function in such that (2.6).

(2) There exist a continuous function and a locally bounded function in such that (2.6) for and as in (1).

Briefly, this means that is locally integrable, and there exists a nonnegative, locally bounded function on such that for all and, where is a set with Lebesgue measure zero.

Suppose that there is a non-zero continuous bounded function M such that M ∈ BM ˜ ( R 2 n ) ( p 1 , p 2 , p 3 . Then 1 ( p 3 ) + ≤ 1 ( p 1 ) − + 1 ( p 2 ) −.

Let be a real Banach space; let be a nonempty closed convex subset of, and let be a Lipschitzian and demicontractive semigroup with a bounded measurable function and a bounded function, respectively, such that (2.1).