KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2025 / Volume: 54 Issue: 6

G-convergence and G-sequential spaces

Shanza Behram(ERCIYES UNIVERSITY)0000-0003-2244-7404
Osman Mucuk(ERCIYES UNIVERSITY)0000-0001-7411-2871
Sayfa
—
Yayın Tarihi
2025-12-30
🏛️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)

Finally, examples of $G$-sequential spaces associated with $G$-methods are given.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, for a method $G$ on a set $X$, we consider $G$-convergence and $G$-sequential convergence; we analyse the distinction between them with some counterexamples.
📊
Temel Bulgular & Veri:Then, $G$-sequential continuity is investigated, and the relations between $G$-continuous and $G$-sequentially continuous functions are determined.
💡
Sonuç & Katkı:Finally, examples of $G$-sequential spaces associated with $G$-methods are given.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:G-method · G-convergence · G-sequential space

Abstract

In this paper, for a method $G$ on a set $X$, we consider $G$-convergence and $G$-sequential convergence; we analyse the distinction between them with some counterexamples. Then, $G$-sequential continuity is investigated, and the relations between $G$-continuous and $G$-sequentially continuous functions are determined. Moreover, $G$-sequential spaces are introduced and studied. Finally, examples of $G$-sequential spaces associated with $G$-methods are given.

🔖

Bu Makaleye Atıf Yap

Behram, S., Mucuk, O. (2025). G-convergence and G-sequential spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 6. https://doi.org/10.15672/hujms.1585422

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (21)

  1. A. Açıkgöz, H. Çakallı, F. Esenbel and L.D.R. Kocinac, A quest of G-continuity in neutrosophic spaces, Mathematical Methods in the Applied Sciences 44 (9), 7834- 7844, 2021.
  2. S. Behram and O. Mucuk, About varieties of G-sequential methods, G-hulls and Gclosures, Proceedings of International Mathematical Sciences 5(2), 81-86, 2023.
  3. J. Connor and K. G. Grosse-Erdmann, Sequential definitions of continuity for real functions, Rocky Mountain J. Math. 33 (1), 93-121, 2003.
  4. H. Çakallı, Sequential definitions of compactness, Appl. Math. Lett. 21 (6), 594-598, 2008.
  5. H. Çakallı, On G-continuity, Comput. Math. Appl. 61, 313-318, 2011.
  6. H. Çakallı, New kinds of continuities, Comput. Math. Appl. 61, 960-965, 2011.
  7. H. Çakallı, Sequential definitions of connectedness, Appl. Math. Lett. 25, 461-465, 2012.
  8. H. Çakallı and O. Mucuk, On connectedness via a sequential method, Revista de la Unión Matemática Argentina 54 (2), 101-109, 2013.
  9. M. Dik and I. Canak, New types of continuities, Abstr. Appl. Anal. 1-7, 2010.
  10. S. Lin and L. Liu, G-methods, G-sequentially spaces and G-continuity in topological spaces, Topology Appl. 212, 29-48, 2016.
  11. L. Liu, G-kernel-open sets, G-kernel-neighbourhoods and G-kernal-derived sets, J. Math. Res. Appl. 38 (3), 276-286, 2018.
  12. G. Di Maio and L.D.R. Kocinac, Statistical convergence in topology, Topology Appl. 156, 28-45, 2008.
  13. O. Mucuk, Topoloji and Kategory Teoreisi, 3rd Edition, Nobel Yayınları, Ankara, 2023. (in Turkish).
  14. O. Mucuk, and S. Behram, Some counter examples of G-convergence, AIP Conference Proceedings-Sixth International Conference of Mathematical Sciences, 2022.
  15. Mucuk, S. Behram and H. Çakallı, G-convergently separation axioms, Filomat 38(18), 6433-6441, 2024.
  16. O. Mucuk and H. Çakallı, G-connectedness for topological groups with operations, Filomat 32 (3), 1079-1089, 2018.
  17. O. Mucuk and H. Çakall, On G-compactness of topological groups with operations, Filomat 36(20), 7113-7121, 2022.
  18. O. Mucuk and T. Sahan, On G-sequential continuity, Filomat 28 (6), 1181-1189, 2014.
  19. O. Mucuk and M.B. Teke, About sequentially open and closed subsets in product spaces, Maltepe Journal of Mathematics 2, 41-46, 2023.
  20. E. Öztürk, On almost-continuity and almost A-continuity of real functions, Commun. Fac. Sci. Univ. Ank. Seér. A1 Math. Stat. 32, 25-30, 1983.
  21. V.K. Srinivasan, An equivalent condition for the continuity of a function, Texas J. Sci. 32, 176-177, 1980.