We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the s...

In answer set programming, knowledge involving sets of objects collectively is naturally represented by aggregates, which are rewritten into simpler forms known as monotone aggregates by current implementations. However, there is a complexity gap between general and monotone aggregates. In this paper, this gap is filled by means of a polynomial, faithful, and modular translation function, which...

In this article we study graph-distance convergence of monotone operators. First, we prove a property that has been an open problem up to now: the limit of a sequence of graph-distance convergent maximal monotone operators in a Hilbert space is a maximal monotone operator. Next, we show that a sequence of maximal monotone operators converging in the same sense in a reflexive Banach space is uni...

and Applied Analysis 3 Example 8. LetX = Z = R, Y = R, and E = F = [0, +∞) ⊂ X and let G,C : E → 2, e : E → Y define as G (u) = {(U, V) : U − u ≤ V ≤ u − U, 0 ≤ U ≤ u} , ∀u ∈ F, C (x) = {(U, V) : 0 ≤ V ≤ ( 3 2 + x)U,U ≥ 0} , ∀x ∈ E, e (x) = (1, 1) , ∀x ∈ E, (7) respectively. We can see that ξ G (x, u) = (1 + (2/(1 + 2x)))u. Definition 9. LetD ⊂ Y be a cone,H : F → 2, and ς : F → R. ς is calledm...

in this paper we propose a descent method for solving variational inequality problems where the underlying operator is nonsmooth, locally Lipschitz, and monotone over a closed, convex feasible set. The idea is to combine a descent method for variational inequality problems whose operators are nonsmooth, locally Lipschitz, and strongly monotone, with the Tikonov-Browder regularization technique....