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Abstract –Korovkin type approximation theorems are useful tools to check whether a given sequence  positive linear operators on  of all continuous functions on the real interval is an approximation process. That is, these theorems exhibit a variety of test functions, which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions and  in the space  as well as for the functions  ,  and in the space of all continuous -periodic functions on the real line. In this paper, we use the notion of weighted  Norlund –Euler statistical convergence to prove the Korovkin approximation theorem for the functions  ,  and in the space of all continuous  -periodic functions on the real line and show that our result is stronger. We also study the rate of weighted  Norlund –Euler statistical convergence.

 

density; statistical convergence; weighted Norlund –Euler statistical convergence; positive linear operator; Korovkin type approximation theorem