On quasi-variational inclusions and asymptotically strict pseudo-contractions. (English) Zbl 1208.47042

The authors study quasi-variational inequalities using a fixed point approach. The main result of the paper is the theorem in which a general iterative process leads to a common element in the zero set of the sum of maximal monotone operators and inverse strongly-monotone mappings. Finally, some special cases concerning Hilbert spaces are discussed.


47H05 Monotone operators and generalizations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J25 Iterative procedures involving nonlinear operators
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47J22 Variational and other types of inclusions