Abstract: This paper constracts some n dimensional nonpositive Rogosinski-type kernal on Rⁿ and some relative nonpositive polynomial approximation operators on the periodic continu ous function space C([-π,π]ⁿ), and has obtained certain higher dimensional Rogosinskitype approximation theorem under the approximate error described by the second order continuous module on this function space.

Key words: Higher dimensional integral kernal, Continuous module, Second order continuous module, C-norm, Rogosinski-type kernal