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Projection iterative methods for extended general variational inequalities. (English) Zbl 1190.49036
Summary: We introduce and study a new class of variational inequalities involving three operators, which is called the extended general variational inequality. Using the projection technique, we show that the extended general variational inequalities are equivalent to the fixed point and the extended general Wiener-Hopf equations. This equivalent formulation is used to suggest and analyze a number of projection iterative methods for solving the extended general variational inequalities. We also consider the convergence of these new methods under some suitable conditions. Since the extended general variational inequalities include general variational inequalities and related optimization problems as special cases, results proved in this paper continue to hold for these problems.

MSC:
49M15Newton-type methods in calculus of variations
49J40Variational methods including variational inequalities
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
93C10Nonlinear control systems
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