In the dynamic programming problem (example 2 32), assume that cent f is bounded on X Atilde X cent G(x) is nonempty for every x X Show that the function T defined by is an operator on the space B(X) (example 2 11) (TB)(x) sup f(x,y) (y)) yeG(x)

Question: In the dynamic programming problem (example 2.32), assume that ¢ f is bounded on X Ã X ¢ G(x) is nonempty for every x X

In the dynamic programming problem (example 2.32), assume that
€¢ f is bounded on X Ã— X
€¢ G(x) is nonempty for every x ˆŠ X
Show that the function T defined by

is an operator on the space B(X) (example 2.11).

(TB)(x) sup {f(x,y) + (y)) yeG(x)

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