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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2010 / Cilt: 39 - Sayı: 4

STATISTICAL FUZZY APPROXIMATION TO FUZZY DIFFERENTIABLE FUNCTIONS BY FUZZY LINEAR OPERATORS

Oktay DUMAN
Sayfa
497–514
Yayın Tarihi
2022-10-18
DOI
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So, we mainly use the notion of A-statistical convergence from summability theory instead of the usual convergence.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we obtain fuzzy approximations to fuzzy differentiable functions by means of fuzzy linear operators whose positivity condition and classical limits fail.
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Temel Bulgular & Veri:In order to get more powerful results than the classical approach we investigate the effects of matrix summability methods on the fuzzy approximation.
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Sonuç & Katkı:So, we mainly use the notion of A-statistical convergence from summability theory instead of the usual convergence.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Korovkin theorem · Statistical convergence · Fuzzy approximation

Abstract

In this paper, we obtain fuzzy approximations to fuzzy differentiable functions by means of fuzzy linear operators whose positivity condition and classical limits fail. In order to get more powerful results than the classical approach we investigate the effects of matrix summability methods on the fuzzy approximation. So, we mainly use the notion of A-statistical convergence from summability theory instead of the usual convergence.

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Bu Makaleye Atıf Yap

DUMAN, O. (2022). STATISTICAL FUZZY APPROXIMATION TO FUZZY DIFFERENTIABLE FUNCTIONS BY FUZZY LINEAR OPERATORS. Hacettepe Journal of Mathematics and Statistics, Cilt: 39 - Sayı: 4, 497–514. https://ajindex.com/articles/530672

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Kaynakça (17)

  1. Altomare, F. and Campiti, M. Korovkin Type Approximation Theory and Its Application (Walter de Gruyter Publ., Berlin, 1994).
  2. Altomare, F. and Rasa, I. Approximation by positive operators in spaces Cp([a, b]), Anal. Num´er. Th´eor. Approx. 18, 1–11, 1989.
  3. Anastassiou, G. A. On basic fuzzy Korovkin theory, Studia Univ. Babe¸s-Bolyai Math. 50, –10, 2005.
  4. Anastassiou, G. A. Higher order fuzzy Korovkin theory via inequalities, Commun. Appl. Anal. 10, 359–392, 2006.
  5. Anastassiou, G. A. and Duman, O. Statistical fuzzy approximation by fuzzy positive linear operators, Comput. Math. Appl. 55, 573–580, 2008.
  6. Anastassiou, G. A. and Duman, O. A Baskakov type generalization of statistical Korovkin theory, J. Math. Anal. Appl. 340, 476–486, 2008.
  7. Boos, J. Classical and Modern Methods in Summability (Oxford University Press, UK, ). Brosowksi, B. A Korovkin-type theorem for differentiable functions, Approximation Theory, III (Proc. Conf., Univ. Texas, Austin, Tex., 1980) (Academic Press, New York-London, ), 255–260.
  8. Delgado, F. J. M., Gonz´ales, V. R. and Morales, D. C. Qualitative Korovkin-type results on conservative approximation, J. Approx. Theory 94, 144–159, 1998.
  9. Dirik, F., Duman, O. and Demirci, K. Statistical approximation to B¨ogel-type continuous and periodic functions, Cent. Eur. J. Math. 7, 539–549, 2009. Do˘gru, O. and Duman, O. Statistical approximation of Meyer-K¨onig and Zeller operators based on q-integers, Publ. Math. Debrecen 68, 199–214, 2006.
  10. Duman, O. Statistical approximation for periodic functions, Demonstratio Math. 36, 873–, 2003.
  11. Duman, O. and Anastassiou, G. A. On statistical fuzzy trigonometric Korovkin theory, J. Comput. Anal. Appl. 10, 333–344, 2008.
  12. Duman, O., Khan, M. K. and Orhan, C. A-Statistical convergence of approximating opera- tors, Math. Inequal. Appl. 6, 689–699, 2003.
  13. Duman, O., Erku¸s, E. and Gupta, V. Statistical rates on the multivariate approximation theory, Math. Comput. Modelling 44, 763–770, 2006. Erku¸s, E. and Duman, O. A Korovkin type approximation theorem in statistical sense, Studia Sci. Math. Hungar. 43, 285–294, 2006. Erku¸s, E. and Duman, O. A-statistical extension of the Korovkin type approximation theo- rem, Proc. Indian Acad. Sci. (Math. Sci.) 115, 499–508, 2005.
  14. Fast, H. Sur la convergence statistique, Colloq. Math. 2, 241–244, 1951.
  15. Freedman, A. R. and Sember, J. J. Densities and summability, Pacific J. Math. 95, 293–305,
  16. Fridy, J. A. On statistical convergence, Analysis 5, 301–313, 1985.
  17. Gal, S. G. Approxima