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Some aspects of extended general variational inequalities. (English) Zbl 1242.49017

Summary: M. A. Noor [“Extended general variational inequalities” Appl. Math. Lett. 22, No. 2, 182-186 (2009; Zbl 1163.49303)], [“Auxiliary principle technique for extended general variational inequalities,” Banach J. Math. Anal. 2, No. 1, 33-39, electronic only (2008; Zbl 1138.49016)] , [“Sensitivity analysis of extended general variational inequalities,” Appl. Math. E-Notes 9, 17-26, electronic only (2009; Zbl 1158.49028)], [“Projection iterative methods for extended general variational inequalities,” J. Appl. Math. Comput. 32, No. 1, 83-95 (2010; Zbl 1190.49036)] introduced and studied a new class of variational inequalities, which is called the extended general variational inequality involving three different operators. This class of variational inequalities includes several classes of variational inequalities and optimization problems. The main motivation of this paper is to review some aspects of these variational inequalities including the iterative methods and sensitivity analysis. We expect that this paper may stimulate future research in this field along with novel applications.

MSC:

49J40 Variational inequalities
47J25 Iterative procedures involving nonlinear operators
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