Research Article
BibTex RIS Cite

Yeni Tip q-Stancu-Durrmeyer Operatörlerinin Lokal Yaklaşım Özellikleri

Year 2024, , 310 - 319, 22.01.2024
https://doi.org/10.47495/okufbed.1324813

Abstract

Bu çalışmada, yeni tip q-Stancu-Durrmeyer operatörleri (q-SD operatörleri) tanımlanmış, bu operatörlerin birinci dereceden ve ikinci dereceden momentleri , için hesaplanmıştır. İkinci dereceden merkezi momenti için de tahmini değer hesaplaması yapılmıştır. İkinci dereceden süreklilik modülü kullanılarak q-SD operatörlerinin lokal yaklaşım özellikleri incelenmiş ve derece Lipschitz sınıfı fonksiyon aracılığıyla tahmini yaklaşım hızı verilmiştir.

References

  • Büyükyazıcı İ. Approximation by Stancu-Chlodowsky polynomials. Comput. and Math. with Appl., 2010; 59(1): 274-282.
  • Büyükyazıcı İ. Direct and converse theorems for generalized Bernstein polynomials based on qintegers. J. App. Func. Anal., 2012; 7(1/2): 81-97.
  • Büyükyazıcı İ., Sharma H. Approximation properties of two dimensional q-Bernstein-Chlodowsky- Durrmeyer operators. Numer. Func. Anal. and Opt., 2012; (12): 1351-1371.
  • Ditzian Z., Totik V. Moduli of smoothness, Springer Verlag, New York, 1987.
  • Durrmeyer JL. Une formule d inversion de la transformee laplace, applications a la theorie des moments. These de 3e cycle, Faculte des Sciences de I Universite de Paris, 1967.
  • Gupta V. Some approximation properties of q-Durrmeyer operators. Appl. Math. Comput. 2008; 197(1): 172-178.
  • Gupta V., Finta Z. On certain q -Durrmeyer type operators. Appl. Math. Comput. 2009, doi: 10.1016/j.amc.2008.12.071.
  • Gupta V., Heping W. The rate of convergence of q-Durrmeyer operators for 0 < q < 1. Math Methods Appl. Sci. 2008; 31(16): 1946-1955.
  • Kac V. Cheung, P. Quantum Calculus. Springer: New York, 2002.
  • Lupas L., Lupas A. Polynomials of binomial type and approximation operators. Studia Univ. BabesBolyai, Mathematica, 1987; (32): 61-69.

Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators

Year 2024, , 310 - 319, 22.01.2024
https://doi.org/10.47495/okufbed.1324813

Abstract

In this article, we propose a new kind of q-Stancu-Durrmeyer operators (or shortly q-SD operators). We calculate first and second order moments, for and we give an estimation for the second order central moment, . Furthermore, through the use of the second modulus of continuity, we invent approximation properties of the q-SD operators in the local sense and by using order Lipschitz kind maximal function, we give a direct estimation for the q-SD operators again in the local sense.

References

  • Büyükyazıcı İ. Approximation by Stancu-Chlodowsky polynomials. Comput. and Math. with Appl., 2010; 59(1): 274-282.
  • Büyükyazıcı İ. Direct and converse theorems for generalized Bernstein polynomials based on qintegers. J. App. Func. Anal., 2012; 7(1/2): 81-97.
  • Büyükyazıcı İ., Sharma H. Approximation properties of two dimensional q-Bernstein-Chlodowsky- Durrmeyer operators. Numer. Func. Anal. and Opt., 2012; (12): 1351-1371.
  • Ditzian Z., Totik V. Moduli of smoothness, Springer Verlag, New York, 1987.
  • Durrmeyer JL. Une formule d inversion de la transformee laplace, applications a la theorie des moments. These de 3e cycle, Faculte des Sciences de I Universite de Paris, 1967.
  • Gupta V. Some approximation properties of q-Durrmeyer operators. Appl. Math. Comput. 2008; 197(1): 172-178.
  • Gupta V., Finta Z. On certain q -Durrmeyer type operators. Appl. Math. Comput. 2009, doi: 10.1016/j.amc.2008.12.071.
  • Gupta V., Heping W. The rate of convergence of q-Durrmeyer operators for 0 < q < 1. Math Methods Appl. Sci. 2008; 31(16): 1946-1955.
  • Kac V. Cheung, P. Quantum Calculus. Springer: New York, 2002.
  • Lupas L., Lupas A. Polynomials of binomial type and approximation operators. Studia Univ. BabesBolyai, Mathematica, 1987; (32): 61-69.
There are 10 citations in total.

Details

Primary Language English
Subjects Numerical Analysis
Journal Section RESEARCH ARTICLES
Authors

Pembe Sabancıgil Özder

Publication Date January 22, 2024
Submission Date July 9, 2023
Acceptance Date November 18, 2023
Published in Issue Year 2024

Cite

APA Sabancıgil Özder, P. (2024). Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 7(1), 310-319. https://doi.org/10.47495/okufbed.1324813
AMA Sabancıgil Özder P. Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators. Osmaniye Korkut Ata University Journal of The Institute of Science and Techno. January 2024;7(1):310-319. doi:10.47495/okufbed.1324813
Chicago Sabancıgil Özder, Pembe. “Local Approximation Properties for the New Type Q-Stancu-Durrmeyer Operators”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7, no. 1 (January 2024): 310-19. https://doi.org/10.47495/okufbed.1324813.
EndNote Sabancıgil Özder P (January 1, 2024) Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7 1 310–319.
IEEE P. Sabancıgil Özder, “Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators”, Osmaniye Korkut Ata University Journal of The Institute of Science and Techno, vol. 7, no. 1, pp. 310–319, 2024, doi: 10.47495/okufbed.1324813.
ISNAD Sabancıgil Özder, Pembe. “Local Approximation Properties for the New Type Q-Stancu-Durrmeyer Operators”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi 7/1 (January 2024), 310-319. https://doi.org/10.47495/okufbed.1324813.
JAMA Sabancıgil Özder P. Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators. Osmaniye Korkut Ata University Journal of The Institute of Science and Techno. 2024;7:310–319.
MLA Sabancıgil Özder, Pembe. “Local Approximation Properties for the New Type Q-Stancu-Durrmeyer Operators”. Osmaniye Korkut Ata Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 7, no. 1, 2024, pp. 310-9, doi:10.47495/okufbed.1324813.
Vancouver Sabancıgil Özder P. Local Approximation Properties for the New Type q-Stancu-Durrmeyer Operators. Osmaniye Korkut Ata University Journal of The Institute of Science and Techno. 2024;7(1):310-9.

23487




196541947019414  

1943319434 19435194361960219721 19784  2123822610 23877

* Uluslararası Hakemli Dergi (International Peer Reviewed Journal)

* Yazar/yazarlardan hiçbir şekilde MAKALE BASIM ÜCRETİ vb. şeyler istenmemektedir (Free submission and publication).

* Yılda Ocak, Mart, Haziran, Eylül ve Aralık'ta olmak üzere 5 sayı yayınlanmaktadır (Published 5 times a year)

* Dergide, Türkçe ve İngilizce makaleler basılmaktadır.

*Dergi açık erişimli bir dergidir.

Creative Commons License

Bu web sitesi Creative Commons Atıf 4.0 Uluslararası Lisansı ile lisanslanmıştır.