SavedAdd your journal

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

LACUNARY STATISTICAL SUMMABILITY OF SEQUENCES OF SETS

Uğur ULUSU
Fatih NURAY
Pages
176–184
Publication Date
2015-10-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data:Also, Wijsman lacunary statistical convergence is compared to other summability methods which are de ned in this paper.
💡
Conclusion & Impact:In addition, we give the relationship between Wijsman lacunary statistical convergence and Hausdorf lacunary statistical convergence.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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.

🔖

Cite This Article

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

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (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.