Continuous dynamic programming approach to inequalities

Abstract

where p and q represent the state and decision vectors, respectively, T represents the transformation of the process, and f(p) represents the optimal return function with initial state p. (Here opt denotes max or min.) Basically, using suitable functional equations of the form (l), lwamoto [9, IO] established a class of classical discrete inequalities by he DP approach, while Wang [ 16, 181 established them by the functional equation approach (e.g., see related references in [ 133 for a more detailed account). Very recently, lwamoto and Wang [ 133 established the Holder,