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Erschienen in:
2014 | OriginalPaper | Buchkapitel
10. Statistical Summability
verfasst von : M. Mursaleen
Erschienen in: Applied Summability Methods
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Abstract
There is another notion of convergence known as the statistical convergence which was introduced by Fast [33] and Steinhaus [93] independently in 1951. In [66], Moricz mentioned that Henry Fast first time had heard about this concept from Steinhaus, but in fact it was Antoni Zygmund who proved theorems on the statistical convergence of Fourier series in the first edition of his book [101, pp. 181–188] where he used the term “almost convergence” in place of statistical convergence and at that time this idea was not recognized much. Since the term “almost convergence” was already in use (as described earlier in this book), Fast had to choose a different name for his concept and “statistical convergence” was most suitable. In this chapter we study statistical convergence and some of its variants and generalizations. Active researches were started after the paper of Fridy [37] and since then many of its generalizations and variants have appeared so far, e.g., [38, 62, 64, 70, 74, 76, 77], and so on.