Sentence examples for is partially bounded from inspiring English sources

If Q is bounded in X, then it is partially bounded in X.

Therefore, A is bounded in X, which further implies that A is partially bounded in X.

Therefore, we get (Vert mathcal{P}xVert leq M_{f}), which shows that (mathcal{P}) is bounded on E and so (mathcal{P}) is partially bounded.

A is partially bounded and it is a partially nonlinear (mathcal{D} -contraction, B is partially continuous anD} -contractionpact, and.

A mapping (Q: Xrightarrow X) is partially bounded if (Q(C)) is bounded for every chain C in X. Q is bounded if (Q(X)) is a bounded subset of X.

Let (A, B: Xrightarrow X) be two nondecreasing operators such that: (a) A is partially bounded and it is a partially nonlinear (mathcal{D} -contraction,   (b) B is partially continuous anD} -contractionpact, and   (c) there exists an element (x_{0}in X) such that (x_{0}leq Ax_{0}+bx_{0}).

Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics.

Step II: In this step, we show that the operator (mathcal{P}) satisfies condition (a) in Theorem 2.1, that is, (mathcal{P}) is a partially bounded and partially nonlinear (mathcal{D} -contraction on E. For this purpose, let (x in E) be arbitrary.

Then by Lemmas 2 and 3, we deduce that A is nondecreasing, partially bounded, and it is a partially nonlinear (mathcal{D} -contraction, anD} -contractionandng, partially continuous, and partially compact.

Then the operator A is nondecreasing, partially bounded, and it is a partially nonlinear (mathcal{mathcal {D}} -contraction in X.

An operator T is said to be uniformly partially bounded if all chains (T(mathcal{C})) in E are bounded by the same constant.