Abstract
A new system of extended general nonlinear regularized nonconvex set‐valued variational inequalities is introduced, and the equivalence between the extended general nonlinear regularized nonconvex set‐valued variational inequalities and the fixed point problems is verified. Then, by this equivalent formulation, a new perturbed projection iterative algorithm with mixed errors for finding a solution of the aforementioned system is suggested and analyzed. Also the convergence of the suggested iterative algorithm under some suitable conditions is proved.
Highlights
Variational inequality theory, introduced by Stampacchia 1, has become a rich source of inspiration and motivation for the study of a large number of problems arising in economics, finance, transportation, network and structural analysis, elasticity, and optimization
The main idea in this technique is to establish the equivalence between the variational inequalities and the fixed point problem using the concept of projection
We establish the equivalence between the extended general nonlinear regularized nonconvex set-valued variational inequalities and the fixed point problems, and by this equivalent formulation, we suggest and analyze a new perturbed projection iterative algorithm with mixed errors for finding a solution of the aforementioned system
Summary
Variational inequality theory, introduced by Stampacchia 1 , has become a rich source of inspiration and motivation for the study of a large number of problems arising in economics, finance, transportation, network and structural analysis, elasticity, and optimization. The main idea in this technique is to establish the equivalence between the variational inequalities and the fixed point problem using the concept of projection. This alternate formulation enables us to suggest some iterative methods for computing the approximate solution; for example, see 5–7, 16–18, 29, 30, 35– 37. We introduce and consider a new system of extended general nonlinear regularized nonconvex set-valued variational inequalities. We establish the equivalence between the extended general nonlinear regularized nonconvex set-valued variational inequalities and the fixed point problems, and by this equivalent formulation, we suggest and analyze a new perturbed projection iterative algorithm with mixed errors for finding a solution of the aforementioned system. We prove the convergence of the suggested iterative algorithm under some suitable conditions
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