Using wavelets for Szász-type operators

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Keywords:

compactly supported wavelets, Szász type operators, second-order Lipschitz continuity, inverse theorems, K-functional
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Abstract

Szász-Mirakjan operators extend the classical Bernstein operators and are useful tools for approximating continuous functions on the infinite interval \([0, \infty)\).
These operators have integral variations of Kantorovich and Durrmeyer types in order to approximate \(L_p\) functions with \(1 \leq p <\infty\), but the integral operators cannot be used to characterize the second-order Lipschitz continuity of continuous functions.
In this paper we introduce a class of Szász type operators by means of Daubechies' compactly supported wavelets. These new operators can be used to characterize the second-order Lipschitz continuity of continuous functions and to approximate \(L_p\) functions.

We also provide direct and inverse theorems of these operators for these purposes.

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References

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Published

1995-08-01

How to Cite

Gonska, H. H., & Zhou, D.-X. (1995). Using wavelets for Szász-type operators. Rev. Anal. Numér. Théor. Approx., 24(1), 131–145. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1995-vol24-nos1-2-art14

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Vol 24, Nos 1-2 (1995)

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