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Start Over Subject statistical convergence

1. A class of statistical and $\sigma$-conservative matrices

Creator:
Çoşkun, Hüsamettin and Çakan, Celal
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
statistical convergence, invariant means, core theorems, and matrix transformations
Language:
English
Description:
In [5] and [10], statistical-conservative and $\sigma $-conservative matrices were characterized. In this note we have determined a class of statistical and $\sigma $-conservative matrices studying some inequalities which are analogous to Knopp’s Core Theorem.
Rights:
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2. Ideal version of Ramsey's theorem

Creator:
Filipów, Rafał, Mrożek, Nikodem, Recław, Ireneusz , and Szuca, Piotr
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
ideal of subsets of natural numbers, Bolzano-Weierstrass theorem, Bolzano-Weierstrass property, ideal convergence, statistical density, statistical convergence, subsequence, monotone sequence, and Ramsey's theorem
Language:
English
Description:
We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations shown in [P. Frankl, R. L. Graham, and V. Rödl: Iterated combinatorial density theorems. J. Combin. Theory Ser. A 54 (1990), 95–111].
Rights:
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3. Lacunary weak statistical convergence

Creator:
Nuray, Fatih
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
weak convergence, statistical convergence, lacunary sequence, and lacunary statistical convergence
Language:
English
Description:
The aim of this work is to generalize lacunary statistical convergence to weak lacunary statistical convergence and I-convergence to weak I-convergence. We start by defining weak lacunary statistically convergent and weak lacunary Cauchy sequence. We find a connection between weak lacunary statistical convergence and weak statistical convergence.
Rights:
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4. Remarks on statistical and I-convergence of series

Creator:
Červeňanský, J., Šalát, T., and Toma, V.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
statistical convergence, I-convergence, and I-convergent serie
Language:
English
Description:
In this paper we investigate the relationship between the statistical (or generally I-convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B. C. Tripathy ''On statistically convergent series'', Punjab. Univ. J. Math. 32 (1999), 1–8, is not correct.
Rights:
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5. Statistical convergence of infinite series

Creator:
Dindoš, M., Šalát, Tibor, and Toma, Vladimír
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
statistical convergence, set of the first category, Hausdorff dimension, and homogeneous set
Language:
English
Description:
In this paper we use the notion of statistical convergence of infinite series naturally introduced as the statistical convergence of the sequence of the partial sums of the series. We will discuss some questions related to the convergence of subseries of a given series.
Rights:
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6. Statistical convergence of subsequences of a given sequence

Creator:
Mačaj, M. and Šalát, T.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
asymptotic density, statistical convergence, Lebesgue measure, Hausdorff dimension, and Baire category
Language:
English
Description:
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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public