Abstract
In this paper, we introduce a regularization method for solving the variational inclusion problem of the sum of two monotone operators in real Hilbert spaces. We suggest and analyze this method under some mild appropriate conditions imposed on the parameters, which allow us to obtain a short proof of another strong convergence theorem for this problem. We also apply our main result to the fixed point problem of the nonexpansive variational inequality problem, the common fixed point problem of nonexpansive strict pseudocontractions, the convex minimization problem, and the split feasibility problem. Finally, we provide numerical experiments to illustrate the convergence behavior and to show the effectiveness of the sequences constructed by the inertial technique.
Highlights
Lemma 2.4 ([16]) Let H and K be two real Hilbert spaces, and let T : K → K be a firmly nonexpansive mapping such that (I – T)x is a convex function from K to R = [–∞, +∞]
Let C be a nonempty closed convex subset of a real Hilbert space H
If A = ∇F and B = ∂G, where ∇F is the gradient of F, and ∂G is the subdifferential of G
Summary
Lemma 2.4 ([16]) Let H and K be two real Hilbert spaces, and let T : K → K be a firmly nonexpansive mapping such that (I – T)x is a convex function from K to R = [–∞, +∞]. Lemma 2.7 ([18] (Demiclosedness principle)) Let C be a nonempty closed convex subset of a real Hilbert space H, and let S : C → C be a nonexpansive mapping with Fix(S) = ∅.
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