Using wavelets for Szász-type operators
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 \le...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
1995-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/521 |
| Summary: | 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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| ISSN: | 2457-6794 2501-059X |