Albanian Journal of Mathematics (ISNN: 1930-1235), Vol 3, No 4 (2009)

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Some classes of general nonconvex variational inequalities.

Muhammad Aslam Noor


In this paper, we introduce and consider a new class of variational inequalities, which is called the general nonconvex variational inequality. We establish the equivalence between the general nonconvex variational inequalities and the fixed point problems as well as the Wiener-Hopf equations using the projection method. This alternative equivalent formulation is used to study 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 suitable conditions. Our method of proofs is very simple as compared with other techniques.

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