Théorème de point fixe et d'approximation. (Fixed point and approximation theorem) (Q1086491)

The paper gives three applications of the notion of minimal point with respect to a subset in a uniformly convex Banach space. In the first part, an equivalent of an ergodic theorem for nonexpansive maps in Hilbert spaces is proved. The second section shows how a Pareto optimum can be approximated by one involving a smaller number of functions. The final part is concerned with cutting corresponding minima with cutting compact sets.