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Iterative methods for solving extended general mixed variational inequalities. (English) Zbl 1228.65104
Summary: We introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.
MSC:
65K15Numerical methods for variational inequalities and related problems
47J20Inequalities involving nonlinear operators
47J25Iterative procedures (nonlinear operator equations)
49J40Variational methods including variational inequalities
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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