© F. Cao and Y. An. 2011
Received: 14 November 2010
Accepted: 17 January 2011
Published: 13 February 2011
2. Main Result
We will show a direct inequality of approximation by the Baskakov-Durrmeyer operator given in (1.10). By means of K-functional and modulus of smoothness defined in , we will extend (1.4) to the case of higher dimension by using a decomposition technique.
In , the following result has been proved.
Now we state the main result of this paper.
Our proof is based on an induction argument for the dimension . We will also use a decomposition method of the operator . We report the detailed proof only for two dimensions. The higher dimensional cases are similar.
which has been proved in 
which can be checked directly and will play an important role in the following proof.
The second inequality of (2.9) has thus been established, and the proof of Theorem 2.2 is finished.
The research was supported by the National Natural Science Foundation of China (no. 90818020).
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