KaydedilenlerDerginizi ekleyin

Dergiler / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 3

Investigations into $\lambda$-Statistical Convergence in $\mathscr{A}$-Metric Spaces

Ramazan Sunar(T.C. MİLLİ EĞİTİM BAKANLIĞI)0000-0001-8107-5618
Sayfa
—
Yayın Tarihi
2026-10-13
🏛️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)

Moreover, the relationships among these concepts are systematically examined.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this study, the concept of statistical convergence in $\mathscr{A}$-metric spaces is revisited and generalized via $(V, \lambda)$-summability.
📊
Temel Bulgular & Veri:Within this framework, the notions of $\lambda$-statistical convergence, $\lambda$-statistical $\mathscr{A}$-Cauchy sequences, and strongly $\mathscr{A}(V,\lambda)$-summable sequences in $\mathscr{A}$-metric spaces are introduced.
💡
Sonuç & Katkı:Moreover, the relationships among these concepts are systematically examined.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$\lambda$-Statistical convergence · Cauchy sequence · $\mathscr{A}$-metric spaces

Abstract

In this study, the concept of statistical convergence in $\mathscr{A}$-metric spaces is revisited and generalized via $(V, \lambda)$-summability. Within this framework, the notions of $\lambda$-statistical convergence, $\lambda$-statistical $\mathscr{A}$-Cauchy sequences, and strongly $\mathscr{A}(V,\lambda)$-summable sequences in $\mathscr{A}$-metric spaces are introduced. Moreover, the relationships among these concepts are systematically examined.

🔖

Bu Makaleye Atıf Yap

Sunar, R. (2026). Investigations into $\lambda$-Statistical Convergence in $\mathscr{A}$-Metric Spaces. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 3. https://doi.org/10.47000/tjmcs.1803585

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (30)

  1. Abazari, R., Statistical convergence in g-metric spaces, Filomat, 36(5)(2022), 1461-1468.
  2. Abbas, M., Ali, B., Suleiman, Y., Yusuf, I., Generalized coupled common fixed point results in partially ordered A -metric spaces, Fixed Point Theory Appl., 2015(1)(2015), 1–24.
  3. Arslan, M., Sunar, R., Rough Convergence in A -metric Spaces, Eur. J. Math. Appl, 3(2023), 13.
  4. Braha, N.L., Tauberian conditions under which λ-statistical convergence follows from statistical summability (V; λ), Miskolc Math. Notes, 16(2)(2015), 695–703.
  5. Connor, J.S., The statistical and strong p-Ces`aro convergence of sequences, Analysis, 8(1-2)(1988), 47–64.
  6. Dhage, B.G., Generalized metric spaces and mapping with fixed point, Bull. Calcutta. Math. Soc., 84(1992), 329–336.
  7. Fast, H., Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
  8. Freedman, A.R., Sember, J.J., Densities and summability, Pacific J. Math., 95(1981), 293–305.
  9. Freedman, A.R., Sember, J.J., Raphael, M., Some Ces´aaro-type summability spaces, Proc. Lond. Math. Soc., 37(1978), 508–520.
  10. Frechet, M.M., Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo (1884-1940), 22(1), 1–72.
  11. Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–313.
  12. Gahler, S., 2-metrische Raume und ihre topologische struktur, Math. Nachr., 26(1963), 115–148.
  13. Gürdal, M., Kolancı, S., Kişi, Ö., Çakal, B, On generalized statistical convergence in g-metric spaces, Ilirias Journal of Mathematics, 10(1)(2023).
  14. Khamsi, M.A., Generalized metric spaces: A survey, J. Fixed Point Theory Appl., 17(3)(2015), 455–475.
  15. Leindler, L. Uber die de la Vallee-Pousinsche Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hungar., 16(1965), 375–387.
  16. Mursaleen, M., λ-statistical convergence, Math. Slovaca, 50(2000), 111–115.
  17. Mustafa, Z., Sims, B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7(2)(2006), 289–297.
  18. Nuray, F., Statistical convergence in 2-metric spaces, J. Class. Anal., 16(2)(2020), 115–123.
  19. Schoenberg, I.J., The integrability of certain functions and related summability methods, Amer. Math. Monthly., 66(1959), 361–375.
  20. Sedghi, S., Shobeand, N., Aliouche, A., A generalization of fixed point theorem in S -metric spaces, Mat. Vesn., 64(3)(2012), 258–266.
  21. Steinhaus, H., Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1951), 73–74.
  22. Sunar, R., Statistical convergence in A -metric spaces, Fundamentals of Contemporary Mathematical Sciences, 5(2)(2024), 83–93.
  23. Sunar, R., A Study On Statistically Localized Sequences in A -metric Spaces, Filomat, 3821(2024), 7389–7397.
  24. Sunar, R., On Deferred Statistical Convergence in A -Metric Spaces, Journal of the Iranian Mathematical Society, 62(2025), e234888.
  25. Sunar, R., Arslan, M., Some Ces`aro–Type and Lacunary Statistical Convergence in A–metric Spaces, J. Class. Anal., 22(1)(2023), 55–66.
  26. Sunar, R., Af -statistical convergence and Af -statistical boundedness by moduli in A -metric spaces, J. Class. Anal., in press.
  27. Yalçın, C., Statistical Convergence on B-Metric Spaces, Turk. J. Math. Comput. Sci,17(1)(2025), 275–281.
  28. Zygmund, A., Trigonometric Series, Cambridge Univ. Press, Cambridge, 1979.
  29. Arslan, M., Sunar, R., Rough Convergence in A -metric Spaces, Eur. J. Math. Appl, 3(2023), 13.
  30. Gürdal, M., Kolancı, S., Kişi, Ö., Çakal, B, On generalized statistical convergence in g-metric spaces, Ilirias Journal of Mathematics, 10(1)(2023).