Displaying similar documents to “Statistical limit point theorems.”

Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu, Halil Gezer (2009)

Open Mathematics

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In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin...

Statistical convergence of subsequences of a given sequence

Martin Máčaj, Tibor Šalát (2001)

Mathematica Bohemica

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This paper is closely related to the paper of Harry I. Miller: Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819 and contains a general investigation of statistical convergence of subsequences of an arbitrary sequence from the point of view of Lebesgue measure, Hausdorff dimensions and Baire’s categories.

Statistical convergence of sequences of functions with values in semi-uniform spaces

Dimitrios N. Georgiou, Athanasios C. Megaritis, Selma Özçağ (2018)

Commentationes Mathematicae Universitatis Carolinae

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We study several kinds of statistical convergence of sequences of functions with values in semi-uniform spaces. Particularly, we generalize to statistical convergence the classical results of C. Arzelà, Dini and P.S. Alexandroff, as well as their statistical versions studied in [Caserta A., Di Maio G., Kočinac L.D.R., {Statistical convergence in function spaces},. Abstr. Appl. Anal. 2011, Art. ID 420419, 11 pp.] and [Caserta A., Kočinac L.D.R., {On statistical exhaustiveness}, Appl....