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Journals / Turkish Journal of Mathematics and Computer Science / 2023 / Cilt: 15 Sayı: 1

On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence

Tuğba YURDAKADİM
Emre TAŞ
Pages
180–183
Publication Date
2023-06-30
DOI
—
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AI Summary & Key Takeaways

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

We have also presented an example to illustrate the strength of our theorem.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:An operator version of the Korovkin theorem has recently been obtained by D.
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Key Findings & Data:With the motivation of this result, we have extended it by using a more powerful convergence which also includes ordinary convergence.
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Conclusion & Impact:We have also presented an example to illustrate the strength of our theorem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Korovkin type approximation · statistical convergence · positive linear operators

Abstract

An operator version of the Korovkin theorem has recently been obtained by D. Popa. With the motivation of this result, we have extended it by using a more powerful convergence which also includes ordinary convergence. We have also presented an example to illustrate the strength of our theorem.

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Cite This Article

YURDAKADİM, T., TAŞ, E. (2023). On Relaxing the Identity Operator in Korovkin Theorem via Statistical Convergence. Turkish Journal of Mathematics and Computer Science, Cilt: 15 Sayı: 1, 180–183. https://ajindex.com/articles/950951

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References (20)

  1. Altomare, F., Campiti, M., Korovkin Type Approximation Theory and Its Applications, De Gruyter Studies in Math., vol.17, de Gruyter&Co, Berlin, 1994.
  2. Atlıhan, Ö.G., Orhan, C., Summation process of positive linear operators, Computers and Mathematics with Appl., 56(2008), 1188–1195.
  3. Atlıhan, Ö.G., Ünver, M., Duman, O., Korovkin theorems on weighted spaces: revisited, Period. Math. Hungar., 75(2017), 201–209.
  4. Bardaro, C., Boccuto, A., Dimitriou, X., Mantellini, I., Abstract Korovkin-type theorems in modular spaces and applications, Cent. Eur. J. Math., 11(2013), 1774–1784.
  5. Connor, J.S., Two valued measures and summability, Analysis, 10(1990), 373–385.
  6. Connor, J.S., R-type summability methods, Cauchy criteria, P-sets and statistical convergence, Proc. Amer. Math. Soc., 115(1992), 319–327.
  7. Duman, O., Khan, M.K., Orhan, C., A-statistical convergence of approximating operators, Math. Inequal. Appl., 6(2003), 689–699.
  8. Duman, O., Orhan, C., Statistical approximation by positive linear operators, Studia Math., 161(2004), 187–197.
  9. Duman, O., Orhan, C., Rates of A-statistical convergence of positive linear operators, Appl. Math. Lett., 18(2005), 1339–1344.
  10. Duman, O. Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(2006), 33–46.
  11. Fast, H., Sur la convergence statistique, In Colloquium mathematicae, 2(1951), 241–244.
  12. Fridy, J.A., On statistical convergence, Analysis, 5(1985), 301–314.
  13. Fridy, J.A., Miller, H.I., Orhan, C., Statistical rates of convergence, Acta Sci. Math., 69(2003), 147–157.
  14. Gadziev, A.D., The convergence problem for a sequence of positive linear operators on unbounded sets, and theorems analogous to that of P. P. Korovkin, Soviet Math. Dokl., 15(1974), 1433–1436.
  15. Gadjiev, A.D., On P.P. Korovkin type theorems, Mat. Zametki, 20(1976), 781–786.
  16. Gadjiev, A.D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain Journal of Math., 32(2002), 129–137.
  17. Korovkin, P.P., On convergence of linear positive operators in the space of continuous functions, Doklady Akad. Nauk SSR., 90(1953), 961–964.
  18. Miller, H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 347(1995), 1811–1819.
  19. Popa, D., An operator version of the Korovkin theorem, J. Math. Anal. Appl., 515(2022), Article No: 126375. Salat, T., On statistically convergent sequences of real numbers, Mat. Slovaca., 30(1980), 139–150.
  20. Unver, M., Orhan, C., Statistical convergence with res