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In this paper we consider a class of monotone mappings underlying many sequential optimization problems over a finite or infinite horizon which are of interest in applications. This class of problems Includes deterministic and stochastic optimal control problems, minimax control problems, Semi-Markov Decision problems and others. We prove some fixed point properties of the optimal value function and we analyze the convergence properties of a related generalized Dynamic Programming algorithm. We also give a sufficient condition for convergence, which is widely applicable and considerably strengthens known related results.