Sentence examples for for the proof of the unique from inspiring English sources
For the proof of the unique determination of the boundary interface (S_{1}) in the inverse scattering problem in the next section, we first study the behavior of the solution v on some part of the boundary interface (S_{1}).
The proof of the unique solvability of problem T ∗ can be found in [7].
As in the proof of the theorem, the mapping has a unique fixed point for each.
The proof of the general quasi-orthogonality (A3), mimics the proof of Proposition 6.1 (see [18, Section 6.5] for details).
The proof of unique solvability is given in Sect.
for all By the proof of Theorem 2.5, there exist unique additive mappings satisfying (3.7) and (3.9).
for all x ∈ A. Proof By the same method as in the proof of Theorem 2.3, there exists a unique ℂ-linear mapping δ : A → A satisfying (3.5).
Proof Following the proof of Theorem 3.1, T and g have a unique coupled common fixed point ( x, y ).
for all x ∈ X and t > 0. Proof By the same reasoning as that in the proof of Theorem 2.1, the mapping D : X → X is a unique ℂ-linear mapping which satisfies (2.10).
The proof of that g is the unique solution to problem (6.1) is similar to the proof of Theorem 2.2.
