Densely relaxed pseudomonotone and quasimonotone generalized variational-like inequalities. (English) Zbl 1462.49024
Authors’ abstract: In this paper, we define the generalized densely relaxed \(\eta-\alpha\) pseudomonotonicity and relaxed \(\eta-\alpha\) quasimonotonicity, and establish the existence of solutions for generalized variational-like inequalities with the above monotonicity notions. The results obtained in this paper improve and generalize many existing results in literature. Furthermore, we give an alternative to some wrong results obtained in literature related to the problem studied in this paper.
Reviewer: Bing Tan (Chengdu)
MSC:
| 49J40 | Variational inequalities |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
Keywords:
variational-like inequalities; densely relaxed \(\eta-\alpha\) pseudomonotonicity; relaxed \(\eta-\alpha\) properly quasimonotonicity; relaxed \(\eta-\alpha\) quasimonotonicity; KKM mappingsReferences:
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