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Applying the Fedosov connections constructed in our previous work, we find a(dense) subsheaf of smooth functions on a K\"ahler manifold $X$ which admits anon-formal deformation quantization. When $X$ is prequantizable and the Fedosovconnection satisfies an integrality condition, we prove that this subsheaf offunctions can be quantized to a sheaf of twisted differential operators (TDO),which is isomorphic to that associated to the prequantum line bundle. We alsoshow that examples of such quantizable functions are given by images of quantummoment maps.

Quantizable functions on K\"ahler manifolds and non-formal quantization