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Zbl 1163.49303
Noor, Muhammad Aslam
Extended general variational inequalities. (English)
[J] Appl. Math. Lett. 22, No. 2, 182-186 (2009). ISSN 0893-9659

Summary: We introduce and consider a new class of general variational inequalities involving three nonlinear operators, which is called the extended general variational inequalities. {\it 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 2000:: *49J40 Variational methods including variational inequalities

Keywords: variational inequalities; nonconvex functions; fixed point problem; convergence; existence

Citations: Zbl 1163.49303

Cited in: Zbl 1191.47081 Zbl 1163.49303

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