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Extended general variational inequalities. (English) Zbl 1163.49303
Summary: We introduce and consider a new class of general variational inequalities involving three nonlinear operators, which is called the extended general variational inequalities. M. Aslam Noor [Appl. Math. Lett. 22, No. 2, 182–186 (2009; Zbl 1163.49303)] has shown that the minimum of nonconvex functions can be characterized via these variational inequalities. Using a projection technique, we establish the equivalence between the extended general variational inequalities and the general nonlinear projection equation. This equivalent formulation is used to discuss the existence of a solution of the extended general variational inequalities. Several special cases are also discussed.

MSC:
49J40 Variational inequalities
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