Korovkin type aproximation theorem through statistical lacunary summability

Korovkin type approximation theorems are useful tools to check whether a given sequence ?????????????? of positive linear operators on ????0,1?? of all continuous functions on the real interval ??0,1?? 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, ?? and ???? in the space ????0,1?? as well as for the functions 1, cos and sin in the space of all continuous 2?-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, ?????? , ???????? in place of 1, ?? and ????. We apply the classical Baskakov operator to construct an example in support of our main result.