Dergiler / Konuralp Journal of Mathematics / 2015 / Cilt: 3 - Sayı: 2

LACUNARY STATISTICAL SUMMABILITY OF SEQUENCES OF SETS

Sayfa
176–184
Yayın Tarihi
2015-10-01
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)

In addition, we give the relationship between Wijsman lacunary statistical convergence and Hausdorf lacunary statistical convergence.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper we de ne the WS􀀀analog of the Cauchy criterion for convergence and show that it is equivalent to Wijsman lacunary statistical convergence.
📊
Temel Bulgular & Veri:Also, Wijsman lacunary statistical convergence is compared to other summability methods which are de ned in this paper.
💡
Sonuç & Katkı:In addition, we give the relationship between Wijsman lacunary statistical convergence and Hausdorf lacunary statistical convergence.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Statistical convergence · lacunary sequence · sequence of sets

Abstract

In this paper we de ne the WS􀀀analog of the Cauchy criterion for convergence and show that it is equivalent to Wijsman lacunary statistical convergence. Also, Wijsman lacunary statistical convergence is compared to other summability methods which are de ned in this paper. After giving new de nitions for convergence, we prove a result comparing them. In addition, we give the relationship between Wijsman lacunary statistical convergence and Hausdorf lacunary statistical convergence.

🔖

Bu Makaleye Atıf Yap

ULUSU, U., NURAY, F. (2015). LACUNARY STATISTICAL SUMMABILITY OF SEQUENCES OF SETS. Konuralp Journal of Mathematics, Cilt: 3 - Sayı: 2, 176–184. https://ajindex.com/articles/786727

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (14)

  1. J.-P. Aubin and H. Frankowska, Set-valued analysis, Birkhauser, Boston, 1990
  2. M. Baronti and P. Papini, Convergence of sequences of sets. In: Methods of Functional Analysis in Approximation Theory, ISNM 76, Birkhauser, Basel, 133-155, 1986
  3. G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Austral. Math. Soc., 31 (1985), 421-432
  4. G. Beer, Wijsman convergence: A survey. Set-Valued Var. Anal., 2 (1994), 77-94
  5. H. Fast, Sur la convergence statistique, Collog. Math., 2 (1951), 241-244
  6. J.A. Fridy, On statistical convergence, Analysis, 5 (1985), 301-313
  7. J.A. Fridy and C. Orhan, Lacunary statistical convergence, Paci c J. Math., 160(1) (1993), 43-51
  8. J.A. Fridy and C. Orhan, Lacunary statistical summability, J. Math. Anal. Appl., 173 (1993), 497-504
  9. F. Nuray and B.E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49 (2012), 87-99
  10. R.E. Powel and S.M. Shah, Summability theory and its applications, Van Nostrand- Rheinhold, London, 1972
  11. I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361-375
  12. U. Ulusu and F. Nuray, Lacunary statistical convergence of sequences of sets, Progress in Applied Mathematics, 4 (2012), 99-109
  13. R.A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70 (1964), 186-188
  14. R. A. Wijsman, Convergence of sequences of Convex sets, Cones and Functions II, Trans. Amer. Math. Soc., 123 (1) (1966), 32-45.