Quantitative uniform approximation by generalized discrete singular operators
Keywords:
Discrete singular operator, modulus of smoothness, uniform convergence.Abstract
Here we study the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular op- erators. We treat both the unitary and non-unitary cases of the operators above. We establish quantitatively the pointwise and uniform convergences of these operators to the unit operator by involving the uniform higher modulus of smoothness of a uniformly continuous function.
Mathematics Subject Classification (2010): 26A15, 26D15, 41A17, 41A25.
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