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.
Normed units in abelian group rings
We compute explicitly the isomorphic structure of the normalized unit group of an abelian group ring under some minimal natural restrictions on the group basis and the coefficient ring. This enlarges affirmations due to Chatzidakis-Pappas (J. London Math. Soc., 1991) and Mollov (Publ. Math. Debrecen, 1971).