Selecting families and their applications
Deguire and Lassonde [P. Deguire, M. Lassonde, Familles selectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261-269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obtain several fixed component theorems of Fan-Browder type, an intersection result, a maximal element theorem for a family of set-valued mappings and a minimax inequality.
Generalizations of the Fan-Browder fixed point theorem and minimax inequalities
In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained.
New fixed point theorems for a family of mappings and applications to problems on sets with convex sections
Some new fixed point theorems for a family of mappings are obtained and applied to problems on sets with convex sections that were first studied by Ky Fan.