Generalized monotonicity – concepts and uses. (English) Zbl 0847.49013

Giannessi, F. (ed.) et al., Variational inequalities and network equilibrium problems. Proceedings of a conference, Erice, Italy, June 19-25, 1994. New York, NY: Plenum, 289-299 (1995).
In this paper, various concepts of generalized monotonicity are presented which are related to generalized convexity concepts. For differentiable operators, many special characterizations are obtained. Using these concepts, two sets of existence results are given for generalized monotone variational inequalities in Banach spaces. Some recent results in the area of generalized monotonicity are reported. This is an outstanding expository paper in this interesting field.
For the entire collection see [Zbl 0834.00044].
Reviewer: M.A.Noor (Riyadh)


49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)