Abstract
We give a method of linear approximation by means of three-diagonal matrices. By this method we modify the Kantorovich operators and obtain a new class of operators which overcomes a difficulty in extending a Berens-Lorentz result to the Kantorvich operators for second order of smoothness. The direct and inverse theorems for these operators in Lp are also presented by the Ditzian-Totik modulus of smoothness.
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