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Zbl 1232.49012
Yao, Yonghong; Noor, Muhammad Aslam; Liou, Yeong-Cheng; Kang, Shin Min
Iterative algorithms for general multivalued variational inequalities. (English)
[J] Abstr. Appl. Anal. 2012, Article ID 768272, 10 p. (2012). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We introduce and study some new classes of variational inequalities and the Wiener-Hopf equations. Using essentially the projection technique, we establish the equivalence between these problems. This equivalence is used to suggest and analyze some iterative methods for solving the general multivalued variational in equalities in conjunction with nonexpansive mappings. We prove a strong convergence result for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general multivalued variational inequalities under some mild conditions. Several special cases are also discussed.

MSC 2000:: *49J40 Variational methods including variational inequalities
49M30 Methods of successive approximation, not based on necessary cond.
49J21
47H09 Mappings defined by "shrinking" properties

Keywords: variational inequalities; Wiener-Hopf equations; general multivalued variational in equalities; nonexpansive mappings; projection technique; iterative methods

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Zentralblatt MATH Berlin [Germany]