Sentence examples for maximal operators see from inspiring English sources

Defining the flow of (mathcal {C}) in the Hilbert space (L^2 X,m)) is now easy, and fits well the classical case of convex functionals on Hilbert spaces or, more generally, of monotone maximal operators (see [22]).

In addition, for other recent research works on approximate proximal point methods and their variants for finding zeros of monotone maximal operators, see, for example, [7 10] and the references therein.

In general, under a certain definiteness condition, a formally differential expression can generate a minimal operator in a related Hilbert space and its adjoint is the corresponding maximal operator (see, e.g., [7, 8]).

This type of mappings is closely related to the resolvent of maximal monotone operators (see [2 4]).

In the literature, many methods have been suggested to solve the variational inclusion problem for maximal monotone operators; see, e.g., [8 12].

Remark 3.2 In an analogous way to Theorem 3.1, we can observe the eigenvalue problem 0 ∈ T x + λ C x for quasibounded perturbations of maximal monotone operators; see [10].

Within the past several decades, many authors have been devoting to the studies on the existence and convergence of zero points for maximal monotone operators; see [38 45] and the references therein.

Within the past several decades, many authors have been devoted to the studies on the existence and convergence of different schemes for zero points for maximal monotone operators; see [3 15] and the references therein.

Moreover, as in our consideration, B is a maximal monotone operator and A is a continuous and monotone operator, we know that the operator (A+B) is a maximal monotone operator (see [21]), and hence one may try to find a solution of the problem (1.9) by using the algorithm (1.7).

Then, we know that is a maximal monotone operator; see [21] for more details.

Using this result, we show a convergence theorem for a maximal monotone operator; see Theorem 3.5.