On multivariate Baskakov operator |
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Authors: | Feilong Cao Chunmei Ding |
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Institution: | a Center of Research for Basic Science, Xi'an Jiaotong University, Xi'an, 710049 Shannxi, PR China b Faculty of Science, China Institute of Metrology, 310018 Hangzhou, Zhejiang, PR China |
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Abstract: | In this paper, we study multivariate Baskakov operator Bn,d(f,x). We first show that the operator can retain some properties of the original function f, such as monotony, semi-additivity and Lipschitz condition, etc. Secondly, we discuss the monotony on the sequence of multivariate Baskakov operator Bn,d(f,x) for n when the function f is convex. Then, we propose, for estimating the rate of approximation, a new modulus of smoothness and prove the modulus to be equivalent to certain K-functional. Finally, with the modulus of smoothness as metric, we establish a strong direct theorem by using a decomposition technique for the operator. |
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Keywords: | Multivariate Baskakov operator Convexity Modulus of smoothness Approximation |
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