Korovkin type aproximation theorem through statistical lacunary summability

Document Type: Regular Paper

Authors

Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Abstract

Korovkin type approximation theorems are useful tools to check whether a given sequence of 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 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  in place of  and  We apply the classical Baskakov operator to construct an example in support of our main result.

Keywords


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