Abstract: This is a functional analysis approach to the seqeuential decision making problems of systems with 

states in a normed linear space. The theory is reconstructed and basic properties such as the existence, uniqueness 

and convergence of solutions are studied at a more general and abstract level. An algorithm, which is comparable 

to Bellman's dynamic programming algorithm and which replaces it is in the case of finite staged sequential decision 

making problems, is proposed. Howard's theory for stochastic problems is generalized to Markovian decision 

making processes in normed spaces.