Abstract. A discrete version of the $\theta $-summability is introduced for higher dimensions. It is proved that the discrete $\theta $-means of a continuous function converge uniformly to the function. Moreover, the multi-dimensional Jackson polynomials converge uniformly to the continuous function.

AMS Subject Classification (1991): 42B08, 46E30, 42A38

Keyword(s): Wiener amalgam spaces, Herz spaces, \theta, discrete-summability, Fejér summability, Jackson polynomials, Hermite interpolation

Received October 14, 2008, and in revised form January 6, 2009. (Registered under 6070/2009.)