Dergiler / Sakarya University Journal of Science / 2018 / Cilt: 22 Sayı: 6

Asymptotically Lacunary I-Invariant Statistical Equivalence of Sequences of Sets Defined By A Modulus Function

Sayfa
1857–1862
Yayın Tarihi
2018-12-01
DOI
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Also, we investigate some relationships among these concepts.

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Amaç & Hipotez:In this paper, we introduce the concepts of strongly asymptotically lacunary I-invariant equivalence, f-asymptotically lacunary I-invariant equivalence, strongly f-asymptotically lacunary I-invariant equivalence and asymptotically lacunary I-invariant statistical equivalence for sequences of sets.
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Temel Bulgular & Veri:In this paper, we introduce the concepts of strongly asymptotically lacunary I-invariant equivalence, f-asymptotically lacunary I-invariant equivalence, strongly f-asymptotically lacunary I-invariant equivalence and asymptotically lacunary I-invariant statistical equivalence for sequences of sets.
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Sonuç & Katkı:Also, we investigate some relationships among these concepts.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Asymptotic equivalence · modulus function · I-convergence

Abstract

In this paper, we introduce the concepts of strongly asymptotically lacunary I-invariant equivalence, f-asymptotically lacunary I-invariant equivalence, strongly f-asymptotically lacunary I-invariant equivalence and asymptotically lacunary I-invariant statistical equivalence for sequences of sets. Also, we investigate some relationships among these concepts.

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Bu Makaleye Atıf Yap

DUNDAR, E., AKIN, N. P., ULUSU, U. (2018). Asymptotically Lacunary I-Invariant Statistical Equivalence of Sequences of Sets Defined By A Modulus Function. Sakarya University Journal of Science, Cilt: 22 Sayı: 6, 1857–1862. https://ajindex.com/articles/942112

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Kaynakça (22)

  1. M. Baronti, and P. Papini, Convergence of sequences of sets, In Methods of functional analysis in approximation theory, ISNM 76, Birkhäuser, Basel, 133-155,1986
  2. G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31, 421–432, 1985
  3. G. Beer, Wijsman convergence: A survey, Set-Valued Anal. 2,77–94, 1994
  4. H. Fast, Sur la convergence statistique, Colloq. Math. 2, 241–244, 1951
  5. J. A. Fridy, On statistical convergence, Analysis, 5, 301–313,1985
  6. J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160(1), 43–51,1993
  7. Ö. Kişi and Nuray, F. A new convergence for sequences of sets, Abstract and Applied Analysis, Article ID 852796, 6 pages, 2013
  8. Ö. Ki▁si, H. Gümü▁s, F. Nuray I-Asymptotically lacunary equivalent set sequences defined by modulus function, Acta Universitatis Apulensis, 41, 141-151,2015
  9. P. Kostyrko, T. Šalát, W. Wilczyński, I-Convergence, Real Anal. Exchange, 26(2), 669–686, 2000
  10. V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Mathematical Sciences. 6(23), 5 pages, 2012
  11. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80, 167–190, 1948
  12. I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100, 161–166, 1986
  13. M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4), 755-762, 1993
  14. M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett., 22, 1700–1704, 2009
  15. M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9, 505–509, 1983
  16. M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math. 10, 457–460, 1979
  17. H. Nakano, Concave modulars, J. Math. Soc. Japan, 5, 29-49, 1953
  18. F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49, 87–99, 2012
  19. F. Nuray, E. Savaş, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math. 10, 267–274, 1994
  20. F. Nuray, H. Gök, U. Ulusu, I_σ-convergence, Math. Commun. 16, 531–538, 2011
  21. N. Pancarog ̆lu, F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications, 3(2), 71–78, 2013
  22. N. Pancaroğlu, F. Nuray, On Invariant Statistically Convergence and Lacunary Invariant Statistically Convergence of Sequences o