Sentence examples for principle to the operator from inspiring English sources

In the classical argument developed by Weth in [14], the maximum principle to the operator (Delta^{2}) under certain boundary conditions and in certain domains is absolutely useful.

We use the Banach contraction principle to prove that the operator has a unique fixed point.

Next, Ran and Reurings [2] extended the Banach contraction principle to continuous monotone operators defined in a partially ordered metric space.

We apply this principle to Hankel integral operators and to infinite Hankel matrices.

Under this principle, both the operator and supplier would have been jointly liable, with no cap on their liability.

Forth, we get a comparison principle for the operator (mathcal{L}).

The second property is the demiclosed principle for the operator (I-T 1-zeta)I-T 1-zetaunder some mI-T 1-zetaons.

In view of condition (3.2), it follows by the Banach contraction mapping principle that the operator (mathcal{L}) is a contraction.

Therefore, we see from the Banach contraction mapping principle that the operator (mathcal{A}) has a fixed point which is the unique solution of the boundary value problem (1.2).

In doing so, the Huygens' principle enables us to obtain the operator equation in a form that involves only finite and non-increasing pre-history of the solution in time.

So, by the fixed point theorem of the contraction mapping principle, the operator T has a unique fixed point, which is the unique solution of the system (1.1).