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Some classes of general nonconvex variational inequalities.

Keywords: Variational inequalities , nonconvex functions , xed-point problem , Wiener-Hopf equations , convergence.

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Abstract:

In this paper, we introduce and consider a new class of variationalinequalities, which is called the general nonconvex variational inequality. Weestablish the equivalence between the general nonconvex variational inequali-ties and the xed point problems as well as the Wiener-Hopf equations usingthe projection method. This alternative equivalent formulation is used tostudy the existence of a solution of the general convex variational inequalities.We also use this equivalence formulation to suggest some iterative methods.Convergence criteria of these new iterative is also discussed under suitableconditions. Our method of proofs is very simple as compared with other tech-niques.

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