A strong convergence theorem for quasi variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mapping and fixed point problems with nonexpansive mappings in Hilbert spaces were discussed.

A new system of generalized set-valued variational inclusions involving A-monotone mappings is given in Hilbert spaces.

An iterative sequence is introduced for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space.