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We study existence and uniqueness of the fixed points solutions of a largeclass of non-linear variable discounted transfer operators associated to asequential decision-making process. We establish regularity properties of thesesolutions, with respect to the immediate return and the variable discount. Inaddition, we apply our methods to reformulating and solving, in the setting ofdynamic programming, some central variational problems on the theory ofiterated function systems, Markov decision processes, discrete Aubry-Mathertheory, Sinai-Ruelle-Bowen measures, fat solenoidal attractors, and ergodicoptimization.

Applications of Variable Discounting Dynamic Programming to Iterated Function Systems and Related Problems