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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

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. Math. Lett....

Statistical convergence of subsequences of a given sequence

Martin Máčaj, Tibor Šalát (2001)

Mathematica Bohemica

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.

Summability "au plus petit terme"

María-Angeles Zurro (1995)

Studia Mathematica

There is a curious phenomenon in the theory of Gevrey asymptotic expansions. In general the asymptotic formal power series is divergent, but there is some partial sum which approaches the value of the function very well. In this note we prove that there exists a truncation of the series which comes near the function in an exponentially flat way.

Summation of series via Laplace transforms.

Anthony Sofo (2002)

Revista Matemática Complutense

We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.

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