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Zbl 1169.49007
Noor, Muhammad Aslam
On a class of general variational inequalities. (English)
[J] J. Adv. Math. Stud. 1, No. 1-2, 75-86 (2008). ISSN 2065-3506; ISSN 2065-5851/e

Summary: We introduce a new class of variational inequalities, which is called the general variational inequality. We also introduce a new class of Wiener-Hopf equations. Essentially using the projection technique, we establish the equivalence between the general variational inequalities and fixed point problems as well as with the Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze some iterative algorithms for solving the general variational inequalities. We also discuss the convergence analysis of these iterative methods. Several special cases are also discussed. Our methods of proofs are very simple as compared with other techniques.

MSC 2000:: *49J40 Variational methods including variational inequalities
90C33 Complementarity problems

Keywords: variational inequalities; nonconvex functions; fixed-point problem; Wiener-Hopf equations; projection operator; convergence

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Zentralblatt MATH Berlin [Germany]