SavedAdd your journal

Journals / TWMS Journal of Applied and Engineering Mathematics / 2018 / Cilt: 8 - Sayı: 1

ON p; q -ANALOG OF STANCU-BETA OPERATORS AND THEIR APPROXIMATION PROPERTIES

M. MURSALEEN
T. KHAN
Pages
136–143
Publication Date
2018-06-01
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)

Also, we study the Voronovskaja type estimate for these operators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we introduce the p; q -analogue of the Stancu-Beta operators and call them as the p; q -Stancu-Beta operators.
📊
Key Findings & Data:We study approximation properties of these operators based on the Korovkin's approximation theorem and also study some direct theorems.
💡
Conclusion & Impact:Also, we study the Voronovskaja type estimate for these operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:q -calculus · Stancu-Beta operators · modulus of continuity

Abstract

In this paper we introduce the p; q -analogue of the Stancu-Beta operators and call them as the p; q -Stancu-Beta operators. We study approximation properties of these operators based on the Korovkin's approximation theorem and also study some direct theorems. Also, we study the Voronovskaja type estimate for these operators.

🔖

Cite This Article

MURSALEEN, M., KHAN, T. (2018). ON p; q -ANALOG OF STANCU-BETA OPERATORS AND THEIR APPROXIMATION PROPERTIES. TWMS Journal of Applied and Engineering Mathematics, Cilt: 8 - Sayı: 1, 136–143. https://ajindex.com/articles/846412

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (14)

  1. Acar T., (2016), (p, q)-generalization of Sz´asz–Mirakyan operators, Math. Meth. Appl. Sci., 39 (10), pp. 2685-2695.
  2. Acar T., Aral A., Mohiuddine S. A., (2016), On Kantorovich modifications of (p, q)-Baskakov opera- tors, J. Inequal. Appl., 2016:98. Acar T., Aral A., Mohiuddine S. A., Approximation by bivariate (p, q)-Bernstein-Kantorovich opera- tors, Iran. J. Sci. Technol. Trans. A Sci., DOI: 10.1007/s40995-016-0045-4.
  3. Aral A., Gupta V., (2012), On the q-analogue of Stancu-Beta operators, Appl. Math. Letters, 25, pp. 67-71.
  4. Cai Q. B., Zhou G., (2016), On (p, q)-analogue of Kantorovich type Bernstein–Stancu–Schurer oper- ators, Appl. Math. Comput., 276, pp. 12-20.
  5. Devore R. A., Lorentz G. G., (1993),
  6. Constructive Approximation, Springer, Berlin. Gadzhiev A. D., (1976), Theorems of the type of P.P. Korovkin type theorems, Math. Zametki, 20 (5), pp. 781-786.
  7. Ilarslan H. G. I. and Acar T., Approximation by bivariate (p, q)-Baskakov–Kantorovich operators, Georgian Math. J., DOI: 10.1515/gmj-2016-0057.
  8. M.N. Hounkonnou, J. Dsir, B. Kyemba, (2013), R(p, q)-calculus: differentiation and integration, SUT Jour. Math., 49(2), pp. 145-167. Lupa¸s A., (1987), A q-analogue of the Bernstein operator, University of Cluj-Napoca, Seminar on Numerical and Statistical Calculus, 9, pp. 85-92.
  9. Mishra V. N., Pandey S., (2016), On Chlodowsky variant of (p, q) Katorovich-Stancu-Schurer opera- tors, Int. J. Anal. Appl., 11(1), pp. 28-39.
  10. Mursaleen M., Alotaibi A., Ansari K. J., (2016), On a Kantorovich variant of (p, q)-Sz´asz-Mirakjan operators, J. Funct. Spaces, 2016, Article ID 1035253, 9 pages. Mursaleen M., Ansari K. J., Khan A., (2016), On (p, q)-analogue of Bernstein operators, Appl. Math. Comput., 266 (2015), pp. 874-882 [Erratum: Appl. Math. Comput., 278, pp. 70-71].
  11. Mursaleen M., Ansari K. J., Khan A., (2015), Some approximation results by (p, q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264 (2015), pp. 392-402 [Corrigendum: Appl. Math. Comput, 269, pp. 744-746].
  12. Mursaleen M., Khan F., Khan A., (2016), Approximation by (p, q) -Lorentz polynomials on a compact disk, Complex Anal. Oper. Theory, 10(8), pp. 1725-1740.
  13. Mursaleen M., Nasiruzzaman Md., Khan A., Ansari K. J., (2016), Some approximation results on Bleimann-Butzer-Hahn operators defined by (p, q) -integers, Filomat, 30(3), pp. 639-648.
  14. Mursaleen M., Nasiuzzaman Md., Nurgali A., (2015), Some approximation results on Bernstein- Schurer operators defined by (p, q)-integers, J. Ineq. Appl., 2015:249