Sentence examples for be a condensing operator from inspiring English sources

Let be a condensing operator on Banach space.

If is continuous and takes bounded, sets into bounded sets, and for every bounded set of with, then is said to be a condensing operator on.

Let Q be a condensing operator

Let Φ be a condensing operator on a Banach space X, that is, Φ is continuous and takes bounded sets into bounded sets, and μ ( Φ ( B ) ) ≤ μ ( B ) for every bounded set B of X with μ ( B ) > 0. If Φ ⊂ ϒ for a convex, closed and bounded set ϒ of X, then Φ has a fixed point in X (where μ denotes Kuratowski's measure of noncompactness).

It is easy to prove that a strict set contraction operator is a condensing operator.

Thus, (Q : B_{r} rightarrow B_{r}) is a condensing operator.

To prove that is a condensing operator, we introduce the decomposition, where (3.7).

Step 4. Now, we prove that (Q: B rightarrow B) is a condensing operator.

Step 4. Now, we prove that (Q : H rightarrow H) is a condensing operator.

Let X be a separable generalized Banach space, and let (F: Omega times Xto X) be a condensing continuous random operator.

Then S is said to be a generalized condensing operator if for any S ⊂ D, α ( S ) ≠ 0 implies α ( A ( S ) ) < α ( S ).