This paper provides sufficient conditions for existence of Markovian equilibrium in models with non-paternalistic altruism extending to one generation ahead. When utility is non-separable, we show that each equilibrium savings policy correspondence is increasing everywhere and single-valued, except perhaps on a countable number of points. It is also upper hemi-continuous where it is single valu...

For realcompact spaces X and Y we give a complete description of the linear biseparating maps between spaces of vector-valued continuous functions on X and Y , where special attention is paid to spaces of vector-valued bounded continuous functions. These results are applied to describe the linear isometries between spaces of vector-valued bounded continuous and uniformly continuous functions.

In a previous paper, the authors defined a new class ofmultiple-valued logic functions, called multiple-valued majority func-tions. This correspondence clarifies the distinction of multiple-valuedmajority functions from multiple-valued threshold functions through thedifference between a number function and an inner product of an inputvector and a weight vector. Zndcx Terns-I...

Throughout this paper, we use intA and CoA to denote the interior and the convex hull of a set A, respectively. Let I be an index set. For each i ∈ I , let Yi, Ei be two Hausdorff topological vector spaces. Consider a family of nonempty convex subsets {Xi}i∈I with Xi ⊆ Ei. Let X = ∏ i∈I Xi and E = ∏ i∈I Ei. An element of the set Xi = ∏ j∈I\i Xi will be denoted by xi; therefore, x ∈ X will be wr...

Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T lZ2 (Received June 30, 1992 and in revised form November 7, 1992) ABSTRACT. A formula is set up between vector-vMued mean and scMax-valued that enbles translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-vMued means, .how tha...