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Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 4

Bivariate Cheney-Sharma operators on simplex

Ayşegül ERENÇİN
Hatice Gül İNCE İLARSLAN
Gülen BAŞCANBAZ TUNCA
Pages
793–804
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

Precisely, we show that these operators preserve Lipschitz condition of a given Lipschitz continuous function $f$ and also the properties of the modulus of continuity functionwhen $f$ is a modulus of continuity function.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider bivariate Cheney-Sharma operators which are not the tensor product construction.
📊
Key Findings & Data:In this paper, we consider bivariate Cheney-Sharma operators which are not the tensor product construction.
💡
Conclusion & Impact:Precisely, we show that these operators preserve Lipschitz condition of a given Lipschitz continuous function $f$ and also the properties of the modulus of continuity functionwhen $f$ is a modulus of continuity function.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Lipschitz continuous function · modulus of continuity function · bivariate Cheney-Sharma operators

Abstract

In this paper, we consider bivariate Cheney-Sharma operators which are not the tensor product construction. Precisely, we show that these operators preserve Lipschitz condition of a given Lipschitz continuous function $f$ and also the properties of the modulus of continuity functionwhen $f$ is a modulus of continuity function.

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Cite This Article

ERENÇİN, A., İLARSLAN, H. G. İ., TUNCA, G. B. (2022). Bivariate Cheney-Sharma operators on simplex. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 4, 793–804. https://ajindex.com/articles/530188

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References (17)

  1. Agratini, O. and Rus, I. A. Iterates of a class of dicsrete linear operators via contraction principle, Comment. Math. Univ. Carolin. 44(3), 555-563, 2003.
  2. Altomare, F. and Campiti, M. Korovkin-type approximaton theory and its applications, (Walter de Gruyter, Berlin-New York, 1994).
  3. Başcanbaz-Tunca, G. and Tuncer, Y. On a Chlodovsky variant of a multivariate beta operator, J. Comput. Appl. Math. 235(16), 4816-4824, 2011.
  4. Başcanbaz-Tunca, G. and Taşdelen, F. On Chlodovsky form of the Meyer-König and Zeller operators, An. Univ. Vest Timiş. Ser. Mat.- Inform. 49(2), 137-144, 2011.
  5. Başcanbaz-Tunca, G., ݝnce-ݝlarslan, H. G. and Erençin, A. Bivariate Bernstein type operators, Appl. Math. Comput. 273, 543-552, 2016.
  6. Başcanbaz-Tunca, G., Erençin, A. and Taşdelen, F. Some properties of Bernstein type Cheney and Sharma operators(accepted). Brown, B.M., Elliott, D. and Paget, D.F. Lipschitz constants for the Bernstein polynomials of a Lipschitz continuous function, J. Approx. Theory 49(2), 196-199, 1987.
  7. Cao, F. Modulus of continuity, K-functional and Stancu operator on a simplex, Indian J. Pure Appl. Math. 35(12), 1343-1364, 2004.
  8. Cao, F., Ding, C. and Xu, Z. On multivariate Baskakov operator, J. Math. Anal. Appl. 307(1), 274-291, 2005. Catinaş, T. and Otrocol, D. Iterates of multivariate Cheney-Sharma operators, J. Comput. Anal. Appl. 15(7), 1240-1246, 2013.
  9. Cheney, E. W. and Sharma, A. On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma 2(5), 77-84, 1964. Craciun, M. Approximation operators constructed by means of Sheer sequences, Rev. Anal. Numér. Théor. Approx. 30(2), 135-150, 2001.
  10. Ding, C. and Cao, F. K-functionals and multivariate Bernstein polynomials, J. Approx. Theory, 155(2), 125-135, 2008.
  11. Erençin, A., Başcanbaz-Tunca, G. and Taşdelen, F. Some preservation properties of MKZ-Stancu type operators, Sarajevo J. Math., 10(22)(1), 93-102, 2014.
  12. Erençin, A., Başcanbaz-Tunca, G. and Taşdelen, F. Some properties of the operators defi ned by Lupaş, Rev. Anal. Numér. Théor. Approx. 43(2), 168-174, 2014.
  13. Farcaş, M. D. About Bernstein polynomials, An. Univ. Craiova Ser. Mat. Inform. 35, 117- 121, 2008.
  14. Khan, M. K. Approximation properties of Beta operators, Progress in approximation theory, (Academic Press,
  15. Boston, MA, 1991), 483-495.
  16. Khan, M. K. and Peters, M. A. Lipschitz constants for some approximation operators of a Lipschitz continuous function, J. Approx. Theory 59(3), 307-315, 1989.
  17. Li, Z. Bernstein polynomials and modulus of continuity