Egorov convergence theorem for measurable set valued mapping s sequence in separable and self reflexive Banach space was studied under various topological convergent meanings,almost everywhere convergent property of measurable set valued mapping sequence was discussed.

On the basis of the definition of set-valued fuzzy Choquet integrals, aiming at the general measurable set-valued mapping, some important properties with respect to this kind of set-valued fuzzy Choquet integrals further were studied , which will extend the applications of this kind of integral theory.

This paper establishes the concept of measurable fuzzy set-valued mapping,elabroates convergences for thesequence of fuzzy set-valued mappings,and presents the integrals of measurable fuzzy set-valued mapping and itspropeties.

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.