Abstract
Korovkin type approximation theorems are useful tools to check whether a given sequence ሺܮ ሻ ஹଵ �of positive linear operators on ܥሾ0,1ሿ of all continuous functions on the real interval ሾ0,1ሿ 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 1,ݔ and ݔ ଶ �in the space ܥሾ0,1ሿ as well as for the functions 1, cos and sin in the space of all continuous 2π-periodic functions on the real line. In this paper, we use the notion of statistical lacunary summability to improve the result of [Ann. Univ. Ferrara, 57(2) (2011) 373-381] by using the test functions 1, ௫� , ଶ௫ in place of 1,ݔ and ݔ ଶ . We
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