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STUDIA MATHEMATICA  Issue no. 4 / 2019  
Article: 
Λ^{2}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, λ^{2}) – summability to generalize the concept of statistical convergence. We call this new method a λ^{2}–statistical convergence and denote by S_{λ}^{2} the set of sequences which are λ^{2}–statistically convergent. We find its relation to statistical convergence and strong (N, λ^{2}) – 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 λ^{2}–statistically summability and the rate of λ^{2}–statistically summability of a sequence of positive linear operators defined from C_{2π}(R) into C_{2π}(R): Mathematics Subject Classification (2010): 40G15, 41A36, 46A45. Keywords: Λ^{2}weighted statistical convergence, Korovkin type theorem, rate of convergence. 
