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Start Over Subject I-convergence

1. I and I∗-convergence in topological spaces

Creator:
Lahir, Benoy Kumar and Das, Pratulananda
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
I-convergence, I ∗ -convergence, condition (AP), I-limit point, and I-cluster poin
Language:
English
Description:
We extend the idea of I-convergence and I ∗ -convergence of sequences to a topological space and derive several basic properties of these concepts in the topological space.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. 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:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Some generalizations of Olivier's theorem

Creator:
Faisant, Alain, Grekos, Georges, and Mišík, Ladislav
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
convergent series, Olivier’s theorem, ideal, I-convergence, and I-monotonicity
Language:
English
Description:
Let ∑ ∞ n=1 an be a convergent series of positive real numbers. L. Olivier proved that if the sequence (an) is non-increasing, then lim n→∞ nan = 0. In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n→∞ nan = 0; Olivier’s theorem is a consequence of our Theorem 2.1. (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the I-convergence, that is a convergence according to an ideal I of subsets of ℕ. Again, Olivier’s theorem is a consequence of our Theorem 3.1, when one takes as I the ideal of all finite subsets of ℕ.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Some remarks on I-faster convergent infinite series

Creator:
Matejíčka, Ladislav
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
I-convergence, I-faster convergent series, and terms of I-convergent series
Language:
English
Description:
A structure of terms of I-faster convergent series is studied in the paper. Necessary and sufficient conditions for the existence of I-faster convergent series with different types of their terms are proved. Some consequences are discussed.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public