KaydedilenlerDerginizi ekleyin

Dergiler / Karaelmas Fen ve Mühendislik Dergisi / 2020 / Cilt: 10 - Sayı: 1

Asymptotically Lacunary $J_\delta$-Equivalence of Sequences of Sets

Küme Dizilerinin Asimptotik Lacunary $J_\delta$ -Denkliği

Esra GÜLLE
Uğur ULUSU
Sayfa
88–93
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also, the relationships among the notions of Wijsman asymptotically lacunary invariant equivalence, Wijsman asymptotically lacunary invariant statistical equivalence, ${\left[{W^L}_{N\delta\theta}\right]}_p$, ${\left[{W^L}_{N\delta\theta}\right]}_p$ and ($W_{J^\ast\delta\vartheta}^L$) are investigated.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, we introduce the notions of Wijsman asymptotically strongly p -lacunary invariant equivalence (${\left[{W^L}_{N\delta\theta}\right]}_p$), Wijsman asymptotically lacunary J -invariant equivalence (${\left[{W^L}_{N\delta\theta}\right]}_p$) and Wijsman asymptotically lacunary J* -invariant equivalence ($W_{J^\ast\delta\vartheta}^L$) for sequences of sets.
📊
Temel Bulgular & Veri:In this study, we introduce the notions of Wijsman asymptotically strongly p -lacunary invariant equivalence (${\left[{W^L}_{N\delta\theta}\right]}_p$), Wijsman asymptotically lacunary J -invariant equivalence (${\left[{W^L}_{N\delta\theta}\right]}_p$) and Wijsman asymptotically lacunary J* -invariant equivalence ($W_{J^\ast\delta\vartheta}^L$) for sequences of sets.
💡
Sonuç & Katkı:Also, the relationships among the notions of Wijsman asymptotically lacunary invariant equivalence, Wijsman asymptotically lacunary invariant statistical equivalence, ${\left[{W^L}_{N\delta\theta}\right]}_p$, ${\left[{W^L}_{N\delta\theta}\right]}_p$ and ($W_{J^\ast\delta\vartheta}^L$) are investigated.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Özet

In this study, we introduce the notions of Wijsman asymptotically strongly p -lacunary invariant equivalence (${\left[{W^L}_{N\delta\theta}\right]}_p$), Wijsman asymptotically lacunary J -invariant equivalence (${\left[{W^L}_{N\delta\theta}\right]}_p$) and Wijsman asymptotically lacunary J* -invariant equivalence ($W_{J^\ast\delta\vartheta}^L$) for sequences of sets. Also, the relationships among the notions of Wijsman asymptotically lacunary invariant equivalence, Wijsman asymptotically lacunary invariant statistical equivalence, ${\left[{W^L}_{N\delta\theta}\right]}_p$, ${\left[{W^L}_{N\delta\theta}\right]}_p$ and ($W_{J^\ast\delta\vartheta}^L$) are investigated.

Abstract

Bu çalışmada, küme dizileri için Wijsman asimptotik kuvvetli p -lacunary invaryant denklik (${\left[{W^L}_{N\delta\theta}\right]}_p$), Wijsman asimptotik lacunary J -invaryant denklik (${\left[{W^L}_{N\delta\theta}\right]}_p$) ve Wijsman asimptotik lacunary J* -invaryant denklik ($W_{J^\ast\delta\vartheta}^L$) kavramları tanıtıldı. Ayrıca, Wijsman asimptotik lacunary invaryant denklik, Wijsman asimptotik lacunary invaryant istatistiksel denklik, ${\left[{W^L}_{N\delta\theta}\right]}_p$, ${\left[{W^L}_{N\delta\theta}\right]}_p$ ve ($W_{J^\ast\delta\vartheta}^L$) kavramları arasındaki ilişkiler araştırıldı.

🔖

Bu Makaleye Atıf Yap

GÜLLE, E., ULUSU, U. (2020). Asymptotically Lacunary $J_\delta$-Equivalence of Sequences of Sets. Karaelmas Fen ve Mühendislik Dergisi, Cilt: 10 - Sayı: 1, 88–93. https://ajindex.com/articles/207156

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (19)

  1. Baronti, M., Papini, P. 1986.
  2. Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory. Birkhäuser, Basel, pp. 133–155.
  3. Beer, G. 1985. On convergence of closed sets in a metric space and distance functions. Bull. Aust. Math. Soc., 31(3): 421–432.
  4. Beer, G. 1994. Wijsman convergence: A survey. Set-Valued Anal., 2(1-2): 77–94.
  5. Fast, H. 1951. Sur la convergence statistique. Colloq. Math., 2(3- 4): 241–244.
  6. Fridy, JA. 1985. On statistical convergence. Analysis, 5(4): 301– 314. Fridy, JA., Orhan, C. 1993. Lacunary statistical convergence. Pacific J. Math., 160(1): 43-51.
  7. Hazarika, B. 2015. On asymptotically ideal equivalent sequences. Journal of the Egyptian Mathematical Society, 23(1): 67–72.
  8. Kişi, Ö., Nuray, F. 2013. New convergence definitions for sequences of sets. Abstract and Applied Analysis, 2013(Article ID 852796): 6 pages. Kostyrko, P., Wilczyński, W., Šalát, T. 2000. J -Convergence. Real Anal. Exchange, 26(2): 669–686.
  9. Marouf, M. 1993. Asymptotic equivalence and summability. Int. J. Math. Math. Sci., 16(4): 755–762.
  10. Mursaleen, M. 1979. Invariant means and some matrix transformations. Tamkang J. Math., 10(2): 183–188.
  11. Mursaleen M., Edely, OHH. 2009. On the invariant mean and statistical convergence. Appl. Math. Lett., 22(11): 1700–1704.
  12. Nuray, F., Gök, H., Ulusu, U. 2011. $J_\delta$ -convergence. Math. Commun., 16: 531–538.
  13. Nuray, F., Rhoades, BE. 2012. Statistical convergence of sequences of sets. Fasc. Math., 49: 87–99.
  14. Pancaroğlu, N., Nuray, F. 2013. On invariant statistically convergence and lacunary invariant statistically convergence of sequences of sets. Progress in Applied Mathematics, 5(2): 23–29.
  15. Pancaroğlu, N., Nuray, F. 2013. Statistical lacunary invariant summability. Theoretical Mathematics and Applications, 3(2): 71–78.
  16. Pancaroğlu, N., Nuray, F., Savaş, E. 2013. On asymptotically lacunary invariant statistical equivalent set sequences. AIP Conf. Proc., 1558(1): 780–781.
  17. Pancaroğlu Akın, N., Dündar, E., Ulusu, U. 2019. Wijsman lacunary J -invariant convergence of sequences of sets. Proc. Nat. Acad. Sci. India Sect. A. (in press). Patterson, R.F., Savaş, E. 2006. On asymptotically lacunary statistically equivalent sequences. Thai J. Math., 4(2): 267–272.
  18. Raimi, R.A. 1963. Invariant means and invariant matrix methods of summability. Duke Math. J., 30(1): 81–94. Šalát, T. 1980. On statistically convergent sequences of real numbers. Math. Slovaca, 30(2): 139–150.
  19. Savaş, E. 1989. Some sequence spaces involvi