Under several suitable transformations, the problem of positive solutions for set-valued condensing mapping equation in an ordered locally convex topological space is studied by some homotopy method.

The problem of the existence of a cone subdifferential for the cone convex set valued maps in the locally convex, linear and topological vector space is discussed.

A collectively fixed point theorem for a family of set-valued mappings defined on a product space of locally generalized convex uniform Spaces is first proved.