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Activated Approximation by Fractional Smooth Singular Operators |
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PP: 225-244 |
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doi:10.18576/pfda/120201
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Author(s) |
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George A. Anastassiou,
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Abstract |
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| In this article we study the fractional smooth activated singular integral operators on the real line, regarding their convergence to the unit operator
with fractional rates in the uniform norm. The related established
inequalities involve the higher order moduli of smoothness of the associated
right and left Caputo fractional derivatives of the engaged function.
Furthermore we produce fractional Voronocskaya type results giving the
fractional asymptotic expansion of the basic error of our approximations.
Our operators are not in general positive. We are mainly motivated and based
on \cite{6}, Chapter 17.
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