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In this chapter 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.

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Activated Quantitative Approximation by Smooth Fractional Singular Operators

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this chapter 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.