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General variational inequalities and nonexpansive mappings. (English) Zbl 1112.49013
Summary: We suggest and analyze some three-step iterative schemes for finding the common elements of the set of the solutions of the Noor variational inequalities involving two nonlinear operators and the set of the fixed-points of nonexpansive mappings. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Since the Noor variational inequalities include variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results.

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators