SavedAdd your journal

Journals / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 4

Approximation by generalized Bernstein–Stancu operators

Nursel ÇETİN
Voichita Adriana RADU
Pages
2032–2048
Publication Date
2022-11-04
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

Finally, the studycontains numerical considerations regarding the constructed operators based on Maple algorithms.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we investigate approximation properties of the Stancu type generalization of the -Bernsteinoperator.
📊
Key Findings & Data:We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity.Also, we present Voronovskaya and Grüss–Voronovskaya type asymptotic results for these operators.
💡
Conclusion & Impact:Finally, the studycontains numerical considerations regarding the constructed operators based on Maple algorithms.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we investigate approximation properties of the Stancu type generalization of the -Bernsteinoperator. We obtain a recurrence relation for moments and the rate of convergence by means of moduli of continuity.Also, we present Voronovskaya and Grüss–Voronovskaya type asymptotic results for these operators. Finally, the studycontains numerical considerations regarding the constructed operators based on Maple algorithms.

🔖

Cite This Article

ÇETİN, N., RADU, V. A. (2022). Approximation by generalized Bernstein–Stancu operators. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 4, 2032–2048. https://ajindex.com/articles/607615

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. Acar T, Acu AM, Manav N. Approximation of functions by genuine Bernstein-Durrmeyer type operators. Journal of Mathematical Inequalities 2018; 12 (4): 975-987
  2. Acar T, Aral A, Raşa I. Positive linear operators preserving and 2. Constructive Mathematical Analysis 2019; 2 (3): 98-102
  3. Acar T, Kajla A. Degree of approximation for bivariate generalized Bernstein type operators. Results in Mathematics 2018; 73: 79. doi: 10.1007/s00025-018-0838-1 [4] Acu AM, Acar T, Radu VA. Approximation by modified U n operators. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales, Serie A Matemáticas 2019; 113: 2715-2729
  4. Acu AM, Gonska HH, Raşa I. Grüss-type and Ostrowski-type inequalities in approximation theory. Ukrainian Mathematical Journal 2011; 63 (6): 843-864
  5. Agratini O. Linear combinations of D.D. Stancu polynomials. Revista de Analiză Numerică și Teoria Aproximației 1998; 27: 15-22
  6. Altomare F, Campiti M. Korovkin-type Approximation Theory and its Applications. New York, NY, USA: Walter de Gruyter, 1994
  7. Bodur M, Yilmaz OG, Aral A. Approximation by Baskakov-Szász-Stancu operators preserving exponential functions. Constructive Mathematical Analysis 2018; 1 (1): 1-8
  8. Campiti M. A generalization of Stancu-Mulbach operators. Constructive Approximation 1991; 7 (1): 1-18
  9. Çetin N. Approximation by complex modified Szasz-Mirakjan-Stancu operators in compact disks. Filomat 2015; 29 (5): 1007-1019
  10. Çetin N. On complex modified genuine Szasz-Durrmeyer-Stancu operators. Communications of the Faculty of Sciences of University of Ankara Series A1-Mathematics and Statistics 2019; 68 (1): 283-298
  11. Chen X, Tan J, Liu Z, Xie J. Approximation of functions by a new family of generalized Bernstein operators. Journal of Mathematical Analysis and Applications 2017; 450: 244-261
  12. Cleciu VA. Bernstein-Stancu operators. Studia Universitatis Babes-Bolyai Mathematica 2007; 52 (4): 53-65
  13. Cleciu VA. Approximation properties of a class of Bernstein-Stancu type operators. In: Agratini O (editor). Proceedings of the International Conference NAAT; Cluj-Napoca, Romania; 2006. pp. 171-178
  14. Della Vechia B. On Stancu operator and its generalizations. Naples, Italy: Inst. Applicazioni della Matematica (Rapp. Tecnico), 1988
  15. Gal S, Gupta V. Approximation by complex Szasz-Mirakyan-Stancu-Durrmeyer operators in compact disks under exponential growth. Filomat 2015; 29 (5): 1127-1136
  16. Gavrea I. On Bernstein-Stancu typ