Sentence examples for be completely continuous and from inspiring English sources

Let operator be completely continuous and satisfy,.

Theorems 2.4 and 2.5 require the operator to be completely continuous and cone preserving.

Let operator T : Ω r → K be completely continuous and satisfy Tx ≠ x, ∀ x ∈ ∂Ω r.

Let P be a cone in a Banach space E, A : P → P be completely continuous, and A θ = θ.

Let be completely continuous, and let be a nonnegative continuous concave functional on such that for all.

Let the operator T : P ∩ Ω r → P be completely continuous and satisfy T x ≠ x, ∀ x ∈ ∂ Ω r.

Hence, the operator is completely continuous and the proof is complete.

Then the operator T λ h is completely continuous, and T λ h K ⊂ K. Proof Firstly, we testify the complete continuity of T λ h.

Lemma 2.6. is completely continuous, and.

So T is completely continuous and the proof is finished.

A is a contraction, B is completely continuous, and.