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    STUDIA MATHEMATICA - Issue no. 1 / 2010  
         
  Article:   STATISTICAL APPROXIMATION BY DOUBLE PICARD SINGULAR INTEGRAL OPERATORS.

Authors:  GEORGE A. ANASTASSIOU, OKTAY DUMAN.
 
       
         
  Abstract:  We first construct a sequence of double smooth Picard singular integral operators which do not have to be positive in general. After giving some useful estimates, we mainly show that it is possible to approximate a function by these operators in statistical sense even though they do not obey the positivity condition of the statistical Korovkin theory.

Key words and phrases. A-statistical convergence, statistical approximation, Picard singular integral operators.
 
         
     
         
         
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