Acta mathematica scientia,Series A ›› 1997, Vol. 17 ›› Issue (3): 285-293.
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Li Song
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Abstract: In this paper, a integral estimation and inverse theorem of weak type in continuous spaces are obtained for Bernstein-Kantorovich operator Knf on a simplex. These will imply,for 0< α< 1 and f ∈ C(S),‖Knf-f‖C(S)=O(n-α)⇔ws2(f,t)C(S)=O(t2α),where ws2(f,t)C(S) is Ditzian-Totik modulus of smoothness.
Key words: Bernstein-Kantorovich operators, Modulus of smoothness
Li Song. The Direct and Inverse Theorems for Multidimensional Bernstein-Kantorovich Operators in C(S)[J].Acta mathematica scientia,Series A, 1997, 17(3): 285-293.
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