Sentence examples for fixed point of operator from inspiring English sources

Conversely, if is fixed point of operator, then direct differentiation gives the proof.

end{aligned} (2.25) Then, by Lemma 2.8 the fixed point of operator T coincides with the solution of BVP (1.1).

From the similar arguments in the proof of Theorem 3.1, we can prove that there exists at least one fixed point of operator in.

By a similar way as the proof of Theorem 3.1, we can prove that there exists at least one fixed point of operator in.

It can be observed that u is a solution of problem (1.4 - 1.6 1.4 - 1.6nly if u is andixed ponly of operator T. We can get the followifg lemma from Lemma 2.1.

Thus, is a fixed point of operator.

However, there are several iterative schemes in the literature for which the fixed points of operators have been approximated over the years by various authors.

Obviously, a positive solution of the boundary value problem (1) and (3) is equivalent to a nonzero fixed point of the operator Q. Next, we will use fixed point index theorem of condensing mapping in cone to seek the nonzero fixed point of Q.

After verifying the compactness of the operator and some necessary a priori estimates for the solutions, we then obtain a fixed point of the operator in a suitable functional space with σ = 1, which is the desired solution of problem (1.1 - 1.3).

Remark 2.13 In Example 2.11 the fixed point of the operator is not unique.

Notice that, which means that the control steers (3.9) from the origin to in time provided that we can obtain a fixed point of the operator.