Received April 29, 1999 / final version received July 21, 2000 Published online September 25, 2000 – c Springer-Verlag & EMS 2000 Abstract. For vector valued maps, convergence in W1 1 and of all minors of the Jacobian matrix in L1 is equivalent to convergence weakly in the sense of currents and in area for graphs. We show that maps defined on domains of dimension n 3 can be approximated strongl...

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

The co-elementary hierarchy is a nested ordinal-indexed sequence of classes of mappings between compacta, with each successor level being defined inductively from the previous one using the topological ultracopower construction. The lowest level is the class of continuous surjections; and the next level up, the coexistential maps, is already a much more restricted class. Co-existential maps are...

The co-elementary hierarchy is a nested ordinalindexed sequence of classes of mappings between compacta, with each successor level being defined inductively from the previous one using the topological ultracopower construction. The lowest level is the class of continuous surjections; and the next level up, the co-existential maps, is already a much more restricted class. Co-existential maps are...

This article studies the numerical approximation of harmonic maps into surfaces, i.e., critical points for the Dirichlet energy among weakly differentiable vector fields that are constrained to attain their pointwise values in a given manifold. An iterative algorithm that is based on a linearization of the constraint about the current iterate at the nodes of a triangulation is devised and its g...

Recently the author [Proc. Amer. Math. Soc. 103(1988), 11291135] proved random versions of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] for continuous condensing random maps and nonexpansive random maps defined on a closed convex bounded subset in a separable Hilbert space. In this paper, we prove that it is still true for (more general) continuous 1-set-contractiv...