On the generalized monotonicity of variational inequalities

Authors:
Min-Ru Bai;Shu-Zi Zhou;Gu-Yan Ni
Affiliations:
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;Department of Mathematics, National University of Defense Technology, Changsha, Hunan 410073, PR China
Venue:
Computers & Mathematics with Applications
Year:
2007

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Abstract

In this paper, three new classes of generalized monotone operators are introduced: the relaxed @m pseudomonotone operator, relaxed @m 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.