Approximation by Complex Generalized Discrete Singular Operators
In this chapter, we work on the general complex-valued discrete singular operators over the real line regarding their convergence to the unit operator with rates in the Lp-norm for 1 ≤ p ≤ ∞. The related established inequalities contain the higher order Lp-modulus of smoothness of the engaged function or its higher order derivative. Also we study the complex-valued fractional generalized discrete singular operators on the real line, regarding their convergence to the unit operator with 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 related function. It follows .
Series on Concrete and Applicable Mathematics
Anastassiou, G., & Kester, M. (2017). Approximation by Complex Generalized Discrete Singular Operators. Series on Concrete and Applicable Mathematics, 20, 127-180. https://doi.org/10.1142/9789813145849_0006