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    STUDIA MATHEMATICA - Issue no. 1 / 2015  
         
  Article:   QUANTITATIVE UNIFORM APPROXIMATION BY GENERALIZED DISCRETE SINGULAR OPERATORS.

Authors:  GEORGE A. ANASTASSIOU.
 
       
         
  Abstract:  Here we study the approximation properties with rates of generalized discrete versions of Picard, Gauss-Weierstrass, and Poisson-Cauchy singular operators. 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.
Keywords: Discrete singular operator, modulus of smoothness, uniform convergence.
 
         
     
         
         
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