Journals / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 2

Kantorovich-Stancu type operators including Boas-Buck type polynomials

Pages
460–471
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we give the figures for comparing approximation properties of the operators $\mathcal{K}_{n}^{(\alpha,\beta)}$ and $\mathcal{B}_{n}.$

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The aim of the paper is to introduce a Kantorovich-Stancu type modification of a generalization of Szász operators defined via Boas-Buck type polynomials and to obtain rates of convergence for these operators.
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Key Findings & Data:The aim of the paper is to introduce a Kantorovich-Stancu type modification of a generalization of Szász operators defined via Boas-Buck type polynomials and to obtain rates of convergence for these operators.
💡
Conclusion & Impact:Furthermore, we give the figures for comparing approximation properties of the operators $\mathcal{K}_{n}^{(\alpha,\beta)}$ and $\mathcal{B}_{n}.$
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Szász operator · modulus of continuity · rate of convergence

Abstract

The aim of the paper is to introduce a Kantorovich-Stancu type modification of a generalization of Szász operators defined via Boas-Buck type polynomials and to obtain rates of convergence for these operators. Furthermore, we give the figures for comparing approximation properties of the operators $\mathcal{K}_{n}^{(\alpha,\beta)}$ and $\mathcal{B}_{n}.$

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Cite This Article

Çekim, B., İçöz, G., Aktaş, R. (2022). Kantorovich-Stancu type operators including Boas-Buck type polynomials. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 2, 460–471. https://ajindex.com/articles/529734

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References (19)

  1. R. Aktaş, B. Çekim and F. Taşdelen, A Kantorovich-Stancu type generalization of Szász operators including Brenke-type polynomials, J. Func. Spaces 2013, 9 pages, 2013.
  2. A. Altın, O. Dogru and F. Tasdelen, The generalization of Meyer-Konig and Zeller operators by generating functions, J. Math. Anal. Appl. 312 (1), 181-194, 2005.
  3. F. Altomare and M. Campiti, Korovkin-type approximation theory and its applica- tions. Appendix A by Michael Pannenberg and Appendix B by Ferdinand Beckhoff, de Gruyter Studies in Mathematics, 17. Walter de Gruyter & Co., Berlin, 1994.
  4. P.L. Butzer, On the extensions of Bernstein polynomials to the infinite interval, Proc. Amer. Soc. 5, 547-553, 1954.
  5. T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978.
  6. A. Ciupa, A class of integral Favard-Szász type operators, Stud. Univ. Babeş-Bolyai Math. 40 (1), 39-47, 1995.
  7. Z. Ditzian and V. Totik, Moduli of Smoothness, Springer-Verlag, New York, 1987.
  8. O. Dogru, M.A. Özarslan and F. Tasdelen, On positive operators involving a certain class of generating functions, Stud. Sci. Math. Hungar. 41 (4), 415-429, 2004.
  9. O. Duman, M.A. Özarslan and B. Della Vecchia, Modified q-Szász-Mirakjan- Kantorovich operators preserving linear functions, Turk. J. Math. 33 (2), 151-158, 2009.
  10. H.W. Gould and A.T. Hopper, Operational formulas connected with two generaliza- tions of Hermite polynomials, Duke Math. J. 29, 51-63, 1962.
  11. M.E.H. Ismail, On a generalization of Szász operators, Mathematica (Cluj), 39, 259- 267, 1974.
  12. M.E.H. Ismail, Classical and quantum orthogonal polynomial in one variable, Cam- bridge University Press,
  13. Cambridge, UK, 2005.
  14. G. İçöz, F. Taşdelen Yeşildal and O. Doğru, Kantrorovich Process of Linear Positive Operators Via Biorthogonal Polynomials, J. Inequal. Spec. Funct. 3, 77-84, 2012.
  15. G. İçöz, F. Taşdelen and S. Varma, On Linear Positive Operators Involving Biorthog- onal Polynomial, Ars Combin. 105, 319-331, 2012.
  16. G. İçöz, S. Varma and S. Sucu, Approximation by operators including generalized Appell polynomials, Filomat 30 (2), 429-440, 2016.
  17. A. Jakimovski and D. Leviatan, Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj) 11, 97-103, 1969.
  18. A. Kajla and P. N. Agrawal, Szász-Kantorovich type operators based on Charlier polynomials, Kyungpook Math. J. 56 (3), 877-897, 2016.
  19. G. Nowak and A. Sikorska-Nowak, Some approximation properties for modified Szász- Mirakyan-Kantorovich operators, Rev. Anal. Numér. Théor. Ap