Abstract
In the last chapter we discussed statistical summability and its various generalizations and variants, e.g., lacunary statistical convergence, λ-statistical convergence, A-statistical convergence, statistical summability (C, 1), and statistical A-summability. In this chapter, we demonstrate some applications of these summability methods in proving Korovkin-type approximation theorems. Such a method was first used by Gadjiev and Orhan [39] in which the statistical version of Korovkin approximation was proved by using the test functions 1, x, and x 2. Since then a large amount of work has been done by applying statistical convergence and its variants, e.g., [61, 71–73, 75, 92] for different set of test functions. In this chapter we present few of them and demonstrate the importance of using these new methods of summability.
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Mursaleen, M. (2014). Statistical Approximation. In: Applied Summability Methods. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-04609-9_11
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DOI: https://doi.org/10.1007/978-3-319-04609-9_11
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