Sentence examples for a unique solution of the functional from inspiring English sources

Then there is a unique solution of the functional equation (1.4).

Hence the mapping has a unique fixed point, which is a unique solution of the functional equation (1.3) in.

It is easy to verify that is also a unique solution of the functional equation (1.3) in.

It follows from (3.16) and Lemma 2.3 that H has a unique fixed point w ∈ B B ( S ), which is also a unique solution of functional equation (1.7).

Thus the Banach fixed point theorem yields that H has a unique fixed point w ∈ B C ( S ), which is a unique solution of functional equation (1.7) in B C ( S ).

for all and for some, then there exists a unique solution function of the functional equation (1.7) such that (3.2). for all.

By virtue of Theorem 2.1, there exists a unique such that and where is a functional defined implicity in (2.24) and. is just a unique solution of (2.12) and is exactly a unique solution of (2.11).

De Sitter's solution showed that Einstein's solution is not a unique solution of his field equations.

(2.3). in a unique manner, which will give rise to a unique solution of (2.2).

We know that the above Tikhonov functional has a unique minimum (w^{delta}_{alpha} x,cdot)) which is the unique solution of the normal equation T^{ast}Tw^{delta}_{alpha}+ alpha^{2} w^{delta}_{alpha}=T^{ast}g^{delta}, quad alpha>0.

Then, converges strongly to the unique solution of the unique solutions of the variational inequality (1.11).