Abstract
In this paper, we studied variational inequalities and fixed point problems in nonconvex cases. By the projection method over prox-regularity sets, the convergence of the suggested iterative scheme was established under some mild rules.
Highlights
Variational inequalities theory, introduced and improved by Stampacchia [1], has a tremendous potential in theoretical research and applied fields
Pang [4] showed that the VIP related to the equilibrium problem can be decomposed into a system of variational inequalities and discussed the convergence of the method of decomposition for a system of variational inequalities
It is worth noticing that the results in [29,30] regarding the iterative schemes for approximating the solutions to variational inequalities are considered in underlying convex sets
Summary
Variational inequalities theory, introduced and improved by Stampacchia [1], has a tremendous potential in theoretical research and applied fields. Studied related iterative schemes for approximating the solutions to systems of variational inequalities. Find v ∈ C1 such that h f (v), w1 − vi ≥ 0, ∀w1 ∈ C1 , and such that u = Av ∈ C2 solves h g(u), w2 − ui ≥ 0, ∀w2 ∈ C2 They suggested some iterative algorithms for approximating the solutions to the SVIP. This problem is an important improvement of the VIP (1). It is worth noticing that the results in [29,30] regarding the iterative schemes for approximating the solutions to variational inequalities are considered in underlying convex sets. In this paper, we extend their results to split systems of nonconvex variational inequalities (SSNVI) in the context of uniformly prox-regular sets, which include the convex sets as special cases
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