The purpose is to present an iterative scheme for finding a common element of the set of solutions of the variational inclusion problem with multi-valued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.

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 system of generalized variational inclusions for set-valued mapping;

The auxiliary principle technique is extended to study a class of generalized strongly nonlinear mixed variational-like inequalities for set-valued mappings without compact values.

Under the conditions of compatibility or sub-compatibility between a set-valued mappingand a single-valued mapping, the existence of cotnnlon fixed points for two set-valued mapping and a single-valued mapping in complete metric space is discussed.

Under the conditions of compatibility or sub-compatibility between a single-valued mapping and a set-valued mapping,a necessary and sufficient condition for set-valued mapping pair and single-valued mapping which have the common fixed point in complete convex metric space are given.

By using the fixed point theorem, they proved the existence theorem of solution for this kind of nonlinear variational Inclusion problem with the set valued mapping in Hilbert spaces.

The purpose is to study the existence of fixed point theories for set valued mappings in B metric space.

The existences of common fixed points and fixed points for set valued mappings in a complete normed space are discussed.