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Zbl 1193.49009
Noor, Muhammad Aslam; Huang, Zhenyu
Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings. (English)
[J] Appl. Math. Comput. 191, No. 2, 504-510 (2007). ISSN 0096-3003

Summary: We introduce and consider a new class of Wiener-Hopf equations involving the nonlinear operator and nonexpansive operators. Essentially using the projection technique we establish the equivalence between the Wiener-Hopf equations and variational inequalities. Using this alternative equivalent formulation, we suggest and analyze an iterative method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solutions of the variational inequalities. We also study the convergence criteria of iterative methods under some mild conditions. Our results include the previous results as special cases and may be considered as an improvement and refinement of the previously known results.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators

Keywords: Wiener-Hopf equations; nonexpansive mappings; relaxed $(\gamma; r)$-cocoercive mappings; variational inequalities

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Zentralblatt MATH Berlin [Germany]