Markov programming by successive approximations with respect to weighted supremum norms

Markovian decision processes are considered in the situation of discrete time, countable state space, and general decision space. By introducing a Banach space with a weighted supremum norm, conditions are derived, which guarantee convergence of successive approximations to the value function. These conditions are weaker then those required by the usual supnorm approach. Several properties of the successive approximations are derived.