Sentence examples for maximal monotone setting from inspiring English sources

In this context, we state the following results before we start examining Theorem 4.7, the main result on linear convergence in the maximal monotone setting.

Let R : H → 2 H be a maximal monotone set-valued mapping.

Then (B_{1}) and (B_{2}) are maximal monotone set-valued mappings.

Assuming that the barrier cone of has nonempty interior, McLinden [34] presented a comprehensive study of the stability of the solution set of the variational inequality, when the mapping is a maximal monotone set-valued mapping.

In this section, we prove a strong convergence theorem for finding a common element of the set of solutions for equilibrium problems, the set of zero points of maximal monotone operators and set of fixed points for strongly relatively nonexpansive mapping in a uniformly convex and uniformly smooth Banach space.

By using Algorithm 1.1, we will find a common element of the set of common zeros of two families of finite maximal monotone mappings, the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping.

In this paper, we introduce and analyze a new general hybrid iterative algorithm for finding a common element of the set of common zeros of two families of finite maximal monotone mappings, the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space.

If U is maximal monotone, then the solution set U-10 is closed and convex.

If M is maximal monotone, then the solution set M - 1 0 is closed and convex.

If A is maximal monotone, then the solution set A-10 is closed and convex.

If B is maximal monotone, then the solution set B − 1 0 is closed and convex.