Multivalued Variational Inequalities with -Pseudomonotone Mappings in Reflexive Banach Spaces

This paper is concerned with the study of a class of variational inequalities with multivalued -pseudomonotone mappings in reflexive Banach spaces by using the -antiresolvent technique. An application to the multivalued nonlinear -complementarity problem is also presented. The results coincide with the corresponding results announced by many others for the gradient state.

Iterative Algorithms for General Multivalued Variational Inequalities

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.