Sentence examples for uniqueness of the operator from inspiring English sources

The existence and uniqueness of the operator follow from the properties of the functional and strict monotonicity of the mapping (see, e.g., [13]).

The existence and uniqueness of the operator Π C follow from the properties of the functional ϕ y, x) and strict monotonicity of the mapping J [17 21].

The existence and uniqueness of the operator follows from the properties of the functional and strict monotonicity of the duality mapping ; for instance, see [20, 27 30].

existence and uniqueness of the operator follow from the properties of the functional and strict monotonicity of the mapping (see, e.g., [2 4]).

The existence and uniqueness of the operator follows from the properties of the functional and strict monotonicity of the mapping (see, e.g., [3, 5 7]).

The existence and uniqueness of the operator follows from some properties of the functional and the strict monotonicity of the mapping (see, e.g., [25 28]).

Necessary and sufficient conditions for the essential uniqueness of the Julia operator of a given transformation are found.

Recalling that T is relatively u-continuous, therefore, as in the proof of Proposition 24, d ( T x, T y ) = dist ( A, B ). Thus, it follows that T ( x ) ∈ B 0 and T ( y ) ∈ A 0. Again, in view of the uniqueness of the projection operator, we have P A ( T ( x ) ) = T ( y ) = T ( P B ( x ) ).

The article establishes the existence and uniqueness of solutions of the operator equations governing the motion of unbounded observables under the Born Markov approximations.

Cancellability of connections can be restated in terms of the uniqueness of certain operator equations as follows.

In [7], Krasnosel'skiĭ gave the concept of concave operators and studied the existence and uniqueness of the fixed point for the operator by the iterative method.