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theorems for combinations and derivatives of Baskakov operators, J. Nanjing Univ. Math. Biquarterly 18 (2001), 251–260. MR 2002k :41034 Xie L. S. Pointwise approximation

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Abstract  

We obtain inequalities for the weighted approximation error of Baskakov type operators and their derivatives. Such inequalities are valid for functions of polynomial growth and are expressed in terms of weighted moduli of continuity.

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It is proved that an integrable functionf can be approximated by the Kantorovich type modification of the Szász—Mirakjan and Baskakov operators inL 1 metric in the optimal order {n −1} if and only ifϕ 2 f′ is of bounded variation where and , respectively.

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, M. , Global approximation theorems for Szász-Mirakyan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J. , 27 (1978), no. 1, 127–142. MR 58 #12116 Becker M

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References [1] Becker , M. 1978 Global approximation theorems for Szász–Mirakjan and Baskakov operators in polynomial weight spaces

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References [1] Becker , M. 1978 Global approximation theorems for Szász—Mirakjan and Baskakov operators in polynomial weight spaces

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-015-0091-2. [6] Becker , M. , Global approximation theorems for Szász—Mirakjan and Baskakov operators in polynomial weight spaces , Indiana Univ. Math. J., , 27 ( 1 ) ( 1978 ), 127 – 142

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