Abstract
The aim of this paper is to propose a new iterative algorithm to approximate the solution for a variational inequality problem in real Hilbert spaces. A strong convergence result for the above problem is established under certain mild conditions. Our proposed method requires the computation of only one projection onto the feasible set in each iteration. Some numerical examples are presented to support that our proposed method performs better than some known comparable methods for solving variational inequality problems.
Highlights
Motivated by the results above, we propose a new algorithm for solving variational inequality problems in real Hilbert spaces
The Picard–Mann method [31], a new algorithm is proposed for solving variational inequality problems in real Hilbert spaces
It is worth mentioning that the proposed method requires the computation of only one projection onto the feasible set in each iteration
Summary
Suppose C is a nonempty closed convex subset of a real Hilbert space H with the inner product h., .i which induces the norm k.k, and A is a self mapping on H. The variational inequality problem (VIP) for an operator A on C ⊂ H is to find a point x ∗ ∈ C such that the following is the case. Published: 1 October 2021 h Ax ∗ , x − x ∗ i ≥ 0 for each x ∈ C. Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
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