## 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.

### MSC:

 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