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A general iterative method with strongly positive operators for general variational inequalities. (English) Zbl 1189.49006
Summary: We introduce and study a general iterative method with strongly positive operators for finding solutions of a general variational inequality problem with inverse-strongly monotone mapping in a real Hilbert space. The explicit and implicit iterative algorithms are proposed by virtue of the general iterative method with strongly positive operators. Under two sets of quite mild conditions, we prove the strong convergence of these explicit and implicit iterative algorithms to the unique common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality problem, respectively.
MSC:
49J40Variational methods including variational inequalities
47J25Iterative procedures (nonlinear operator equations)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
65K15Numerical methods for variational inequalities and related problems
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
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