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    STUDIA MATHEMATICA - Issue no. 4 / 2019  
         
  Article:   Λ2-STATISTICAL CONVERGENCE AND ITS APPLICATION TO KOROVKIN SECOND THEOREM.

Authors:  VALDETE LOKU, NAIM L. BRAHA.
 
       
         
  Abstract:  
In this paper, we use the notion of strong (N, λ2) – summability to
generalize the concept of statistical convergence. We call this new method a λ2–statistical convergence and denote by Sλ2 the set of sequences which are λ2–statistically convergent. We find its relation to statistical convergence and strong (N, λ2) – summability. We will define a new sequence space and will show that it is Banach space. Also we will prove the second Korovkin type approximation theorem for λ2–statistically summability and the rate of λ2–statistically summability of a sequence of positive linear operators defined from C(R) into C(R):

Mathematics Subject Classification (2010): 40G15, 41A36, 46A45.

Keywords: Λ2-weighted statistical convergence, Korovkin type theorem, rate of convergence.
 
         
     
         
         
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