ON EPSILON-OPTIMAL CONTINUOUS SELECTORS AND THEIR APPLICATION IN DISCOUNTED DYNAMIC-PROGRAMMING

Let X, Y be topological spaces, phi :X yields 2**Y a multifunction, and u a real-valued function defined on the graph of phi . We give sufficient conditions for the existence of a continuous selector f for phi such that u(x,f(x)) greater than equivalent to sup left brace u(x,y): y an element of phi (x) left brace minus epsilon , x an element of X, where epsilon greater than 0. This result is applied to the stochastic discounted dynamic programming problem. We establish the existence of an epsilon -optimal continuous stationary policy.