Journals / Konuralp Journal of Mathematics / 2020 / Cilt: 8 - Sayı: 1

$f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences

Pages
207–210
Publication Date
2020-04-15
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Also, we investigate some relationships among them.

📌 3 Key Takeaways

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Objective & Hypothesis:In this study, we present the notions of strongly asymptotically $\mathcal{I}$-invariant equivalence, $f$-asymptotically $\mathcal{I}$-invariant equivalence, strongly $f$-asymptotically $\mathcal{I}$-invariant equivalence and asymptotically $\mathcal{I}$-invariant statistical equivalence for real sequences.
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Key Findings & Data:In this study, we present the notions of strongly asymptotically $\mathcal{I}$-invariant equivalence, $f$-asymptotically $\mathcal{I}$-invariant equivalence, strongly $f$-asymptotically $\mathcal{I}$-invariant equivalence and asymptotically $\mathcal{I}$-invariant statistical equivalence for real sequences.
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Conclusion & Impact:Also, we investigate some relationships among them.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ideal · Asymptotically equivalence · $\mathcal{I}$-equivalence

Abstract

In this study, we present the notions of strongly asymptotically $\mathcal{I}$-invariant equivalence, $f$-asymptotically $\mathcal{I}$-invariant equivalence, strongly $f$-asymptotically $\mathcal{I}$-invariant equivalence and asymptotically $\mathcal{I}$-invariant statistical equivalence for real sequences. Also, we investigate some relationships among them.

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Cite This Article

DUNDAR, E., AKIN, N. (2020). $f$-Asymptotically $\mathcal{I}_{\sigma}$-Equivalence of Real Sequences. Konuralp Journal of Mathematics, Cilt: 8 - Sayı: 1, 207–210. https://ajindex.com/articles/786474

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References (23)

  1. J.S. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull. 32 (1989), 194-198
  2. H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241–244
  3. E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, TartuUl. Toimetised, 960 (1993), 41-50
  4. P. Kostyrko, T. Salat, W. Wilczynski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686
  5. V. Kumar, A. Sharma, Asymptotically lacunary equivalent sequences defined by ideals and modulus function, Mathematical Sciences, 6(23) (2012), 5 pages
  6. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167–190
  7. I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–166
  8. M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Math. Sci. 16(4) (1993), 755-762
  9. M. Mursaleen, O. H. H. Edely, On the invariant mean and statistical convergence, Appl. Math. Lett. 22 (2009), 1700–1704
  10. M. Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math. 9 (1983), 505–509
  11. M. Mursaleen, On finite matrices and invariant means, Indian J. Pure and Appl. Math. 10 (1979), 457–460
  12. H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29-49
  13. F. Nuray, E. Savas¸, Invariant statistical convergence and A-invariant statistical convergence, Indian J. Pure Appl. Math. 10 (1994), 267–274
  14. F. Nuray, H. G¨ok, U. Ulusu, Is -convergence, Math. Commun. 16 (2011), 531–538
  15. N. Pancaroˇglu, F. Nuray, Statistical lacunary invariant summability, Theoretical Mathematics and Applications, 3(2) (2013), 71–78
  16. R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Mathematica, 36(1) (2003), 149–153
  17. S. Pehlivan, B. Fisher, Some sequences spaces defined by a modulus, Mathematica Slovaca, 45 (1995), 275-280
  18. R. A. Raimi, Invariant means and invariant matrix methods of summability, Duke Math. J. 30 (1963), 81–94
  19. E. Savas¸, Some sequence spaces involving invariant means, Indian J. Math. 31 (1989), 1–8
  20. E. Savas¸, Strong s-convergent sequences, Bull. Calcutta Math. 81 (1989), 295–300
  21. E. Savas¸, F. Nuray, On s-statistically convergence and lacunary s-statistically convergence, Math. Slovaca, 43(3) (1993), 309–315
  22. P. Schaefer, Infinite matrices and invariant means, Proc. Amer. Math. Soc. 36 (1972), 104–110
  23. I. J. Schoenberg, The in