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Abstract

We present direct and strong converse theorems for a general sequence of positive linear operators satisfying some functional equations. The results can be applied to some extensions of Baskakov and Szász–Mirakyan operators.

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Abstract  

Recently P. Mache and M. W. Müller introduced the Baskakov quasi-interpolants and obtained an approximation equivalence theorem. In this paper we consider simultaneous approximation equivalence theorem for Baskakov quasi-interpolants.

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In this paper we give the direct, inverse and equivalence theorems for generalization Meyer-König and Zeller type operators in the space L p (1 ≦ p ) with Ditzian-Totik modulus.

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Abstract

The uniform weighted approximation errors of Baskakov-type operators are characterized for weights of the form for γ 0,γ ∊[−1,0]. Direct and strong converse theorems are proved in terms of the weighted K-functional.

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Abstract

Best trigonometric approximation in L p, 1≦p≦∞, is characterized by a modulus of smoothness, which is equivalent to zero if the function is a trigonometric polynomial of a given degree. The characterization is similar to the one given by the classical modulus of smoothness. The modulus possesses properties similar to those of the classical one.

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