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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 5

Some new insights into ideal convergence and subsequences

Leila MİLLER-VAN WİEREN
Emre TAŞ
Tuğba YURDAKADİM
Sayfa
1379–1384
Yayın Tarihi
2022-10-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Some of them are easily derived from earlier results but they offer some new deeper insights.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Some results on the sets of almost convergent, statistically convergent, uniformly statistically convergent, $I$-convergent subsequences of $(s_{n})$ have been obtained by many authors via establishing a one-to-one correspondence between the interval $(0,1]$ and the collection of all subsequences of a given sequence $s=(s_{n})$.
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Temel Bulgular & Veri:However, there are still some gaps in the existing literature.
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Sonuç & Katkı:Some of them are easily derived from earlier results but they offer some new deeper insights.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:ideal convergence · subsequences · I-cluster and I-limit points

Abstract

Some results on the sets of almost convergent, statistically convergent, uniformly statistically convergent, $I$-convergent subsequences of $(s_{n})$ have been obtained by many authors via establishing a one-to-one correspondence between the interval $(0,1]$ and the collection of all subsequences of a given sequence $s=(s_{n})$. However, there are still some gaps in the existing literature. In this paper we plan to fill some of the gaps with new results. Some of them are easily derived from earlier results but they offer some new deeper insights.

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Bu Makaleye Atıf Yap

WİEREN, L. M., TAŞ, E., YURDAKADİM, T. (2022). Some new insights into ideal convergence and subsequences. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 5, 1379–1384. https://ajindex.com/articles/669157

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Kaynakça (21)

  1. V. Balaz and T. Šalát, Uniform density $u$ and corresponding $I_{u}$- convergence, Math. Commun. 11, 1-7, 2006
  2. M. Balcerzak, S. Glab and A. Wachowicz, Qualitative properties of ideal convergent subsequences and rearrangements Acta Math. Hungar. 150, 312-323, 2016
  3. M. Balcerzak, S. Glab and P. Leonetti, Another characterization of meager ideals, submitted for publication, 2021
  4. M. Balcerzak and P. Leonetti, On the relationship between ideal cluster points and ideal limit points, Topology and Appl. 252, 178-190, 2019
  5. M. Balcerzak and P. Leonetti, The Baire category of subsequences and permutations which preserve limit points, Results Math. 121, 2020
  6. P. Billingsley, Probability and measure, Wiley, New york, 1979
  7. R.C. Buck and H. Pollard, Convergence and summability properties of subsequences, Bull. Amer. Math. Soc. 49, 924-931, 1943
  8. K. Demirci, I-limit superior and inferior, Math. Commun. 6, 165-172, 2001
  9. I. Farah, Analytic quotients. Theory of lifting for quotients over analytic ideals on integers, Mem. Amer. Math. Soc. 148, xvi+177 pp, 2000
  10. H. Fast, Sur la convergence statistique, Colloq. Math. 2, 241-244, 1951
  11. J.A. Fridy, Statistical limit points, Proc. Amer. Math. Soc. 118, 1187-1192, 1993
  12. X. He, H. Zhang, S. Zhang The Borel complexity of ideal limit points, Topology and Appl. 312, 2022
  13. T.A. Keagy, Summability of certain category two classes, Houston J. Math. 3, 61-65, 1977
  14. P. Kostyrko, T. Šalát and W. Wilczyński, $I$-convergence, Real Anal. Exchange, 26, 669-686, 2000/2001
  15. P. Leonetti, H.I. Miller and L. Miller-Van Wieren, Duality between measure and category of almost all subsequences of a given sequences, Period. Math. Hungar. 78, 152-156, 2019
  16. P. Leonetti, Thinnable ideals and invariance of cluster points, Rocky Mount. J. Math. 48(6), 2018
  17. P. Leonetti, Invariance of ideal limit points, Topology and Appl. 252, 169-177, 2019
  18. L. Miller-Van Wieren, E. Taş and T. Yurdakadim, Category theoretical view of Icluster and I-limit points of subsequences, Acta Comment. Univ. Tartu. Math. 24, 103-108, 2020
  19. H.I. Miller and C. Orhan, On almost convergence and statistically convergent subsequences, Acta. Math. Hungar. 93, 135-151, 2001
  20. H.I. Miller and L. Miller-Van Wieren, Some statistical cluster point theorems, Hacet. J. Math. Stat. 44, 1405-1409, 2015
  21. H.I. Miller and L. Miller-Van Wieren, Statistical cluster point and statistical limit point sets of sub