Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 68 Issue: 1

On Complex Modified Genuine Szász-Durrmeyer-Stancu Operators

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Publication Date
2019-02-01
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⚡ TL;DR(Too Long; Didn't Read)

We obtain some estimates on the rate of convergence, a Voronovskaja-type result and the exact order of approximation for these operators attached to analytic functions of exponential growth on compact disks.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we introduce complex modified genuine Szász-Durrmeyer-Stancu operators to improve the results obtained in [4] and present overconvergence properties of these operators.
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Key Findings & Data:In this paper, we introduce complex modified genuine Szász-Durrmeyer-Stancu operators to improve the results obtained in [4] and present overconvergence properties of these operators.
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Conclusion & Impact:We obtain some estimates on the rate of convergence, a Voronovskaja-type result and the exact order of approximation for these operators attached to analytic functions of exponential growth on compact disks.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Complex genuine Szász-Durrmeyer-Stancu operators · overconvergence · simultaneous approximation

Abstract

In this paper, we introduce complex modified genuine Szász-Durrmeyer-Stancu operators to improve the results obtained in [4] and present overconvergence properties of these operators. We obtain some estimates on the rate of convergence, a Voronovskaja-type result and the exact order of approximation for these operators attached to analytic functions of exponential growth on compact disks.

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Cite This Article

Çetin, N. (2019). On Complex Modified Genuine Szász-Durrmeyer-Stancu Operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 1. https://doi.org/10.31801/cfsuasmas.415926

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References (24)

  1. Agrawal P.N. and Gupta V., On convergence of derivatives of Phillips operators, Demonstratio Math. 27 (2), 501-510 (1994).
  2. Bernstein S. N., Sur la convergence de certaines suites des polynomes, J. Math. Pures Appl. 15(9), 345-358 (1935).
  3. Çetin N., Approximation by complex modified Szász-Mirakjan-Stancu operators in compact disks, Filomat, 29 (5), 1007-1019 (2015).
  4. Çetin N. and İspir N., Approximation properties of complex modified genuine Szász-Durrmeyer operators, Comput. Methods Funct. Theory (2014) 14:623-638.
  5. Deeba E. Y., On the convergence of generalized Szasz operator on complex plane, Tamkang J. Math. 13 (1982), no. 1, 79--86.
  6. Finta Z., Gupta V., Direct and inverse estimates for Phillips type operators, J. Math. Anal. Appl. 303 (2) (2005), 627-642.
  7. Gal S. G., Approximation by Complex Bernstein and Convolution Type Operators, Series on Concrete and Applicable Mathematics, 8. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2009. xii+337 pp. ISBN: 978-981-4282-42-0.
  8. Gal S. G., Approximation by complex genuine Durrmeyer type polynomials in compact disks, Appl. Math. Comput. 217 (2010) 1913-1920.
  9. Gal S. G., Gupta V., Approximation by Complex Durrmeyer Type Operators in Compact Disks, Mathematics Without Boundaries, in:P. Pardalos, T.M. Rassias (Eds.), Surveys in Interdisciplinary Research, Springer, 2014.
  10. Gergen J. J., Dressel F. G. and Purcell W.H., Convergence of extended Bernstein polynomials in the complex domain, Pacific J. Math. 13 (4) (1963) 1171-1180.
  11. Gupta V., Tachev G., Approximation by linear combinations of complex Phillips operators in compact disks, Results. Math., DOI 10.1007/s00025-014-0377-3.
  12. Gupta V. and Verma D. K., Approximation by complex Favard-Szász-Mirakjan-Stancu operators in compact disks, Mathematical Sciences 6:25 (2012).
  13. Gupta V., Complex Baskakov-Szász operators in compact semi-disks, Lobachevskii J. Math. 35(2), 65-73 (2014).
  14. Heilmann M., Tachev G., Commutativity, direct and strong converse results for Phillips operators, East J. Approx. 17(3) (2011) 299-317.
  15. Jakimovski A. and Leviatan D., Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj), 34 (1969), 97-103.
  16. Kantorovich L. V., Sur la convergence de la suite de polynomes de S. Bernstein en dehors de l'interval fundamental. Bull. Acad. Sci. URSS 1103-1115 (1931).
  17. Lorentz G. G., Bernstein Polynomials, 2nd ed., Chelsea Publ., New York (1986).
  18. May C.P., On Phillips operator, J. Approx. Theory 20, 315-332 (1977).
  19. Mazhar S.M., Totik V., Approximation by modified Szász operators, Acta Sci. Math. 49 (1985), 257-269.
  20. Phillips R. S., An inversion formula for semi-groups of linear operators, Ann. Math. 59 (1954) 352--356.
  21. Tonne, P.C., On the convergence of Bernstein polynomials for some unbounded analytic functions, Proc. Am. Math. Soc., 22,1-6.
  22. Wood B., Generalized Szász operators for the approximation in the complex domain, SIAM J. Appl. Math., 17(4), (1969), 790--801.
  23. Wright E. M., The Bernstein approximation polynomials in the complex plane, J. Lond. Math. Soc. 5, 265-269 (1930).
  24. Gupta V., Tachev G., Approximation by linear combinations of complex Phillips operators in compact disks, Results. Math., DOI 10.1007/s00025-014-0377-3.