On the generalized monotonicity of variational inequalities. (English) Zbl 1122.49006

Bai, Min-Ru; Zhou, Shu-Zi; Ni, Gu-Yan

Comput. Math. Appl. 53, No. 6, 910-917 (2007).

Summary: Three new classes of generalized monotone operators are introduced: the relaxed \(\mu \) pseudomonotone operator, relaxed \(\mu \) quasimonotone operator and densely relaxed pseudomonotone operator. The relations between these three classes and the relations between them and some other well known classes of generalized monotone operators are discussed in detail. Various existence results for variational inequalities in normed spaces are derived. The results generalize some known results.

MSC:

49J40	Variational inequalities
47J20	Variational and other types of inequalities involving nonlinear operators (general)
65K10	Numerical optimization and variational techniques

Keywords:

variational inequality; relaxed \(\mu\); pseudomonotone; densely relaxed \(\mu\); quasimonotone; existence result

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