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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 73 Issue: 3

On the eigenstructure of the q-Stancu operator

Övgü Gürel Yılmaz(RECEP TAYYIP ERDOGAN UNIVERSITY)0000-0003-1498-8526
Sayfa
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Yayın Tarihi
2024-09-27
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In addition, for special choices of parameters, several eigenfunctions are depicted.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, $L_{n,s,q}$, introduced by $L$.
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Temel Bulgular & Veri:Further, it has been proved that $L_{n,s,q}$ possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived.
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Sonuç & Katkı:In addition, for special choices of parameters, several eigenfunctions are depicted.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:q-integers · q-Stirling numbers · q-Stancu operators

Abstract

The main goal of this research is to find the eigenvalues and the corresponding eigenfunctions of the q-Stancu operator, $L_{n,s,q}$, introduced by $L$. Yun and R. Wang. In this work, an explicit representation for moments of all orders has been derived. Further, it has been proved that $L_{n,s,q}$ possesses $n − s + 1$ linearly independent eigenfunctions whose explicit expression and the corresponding eigenvalues are derived. In addition, for special choices of parameters, several eigenfunctions are depicted.

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Bu Makaleye Atıf Yap

Yılmaz, Ö. G. (2024). On the eigenstructure of the q-Stancu operator. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 3. https://doi.org/10.31801/cfsuasmas.1388792

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Kaynakça (21)

  1. Andrews, G. E., Askey, R., Roy, R., Special Functions, Encyclopedia of Mathematics and Its Applications, The University Press, Cambridge, 1999, 664 pp.
  2. Bernstein, S. N., Demonstration du theoreme de Weierstrass fondee sur le calcul of probabilites, Comm. Kharkov Math. Soc., 13 (1912), 1-2.
  3. Bostanci, T., Başcanbaz-Tunca, G., On Stancu operators depending on a non-negative integer, Filomat, 36(18) (2022), 6129-6138. https://doi.org/10.2298/FIL2218129B
  4. Cooper, S., Waldron, S., The eigenstructure of the Bernstein operator, J. Approx. Theory, 105(1) (2000), 133-165. https://doi.org/10.1006/jath.2000.3464
  5. Goodman, T. N. T., Oruç, H., Phillips, G. M., Convexity and generalized Bernstein polynomials, Proc. Edinburgh Math. Soc., 42(1) (1999), 179-190. https://doi.org/10.1017/S0013091500020101
  6. Gordon, W. J., Riesenfeld, R. F., Bernstein–Bezier methods for the computer-aided design of free-form curves and surfaces, J. Assoc. Comput. Mach., 21(2) (1974), 293-310. https://doi.org/10.1145/321812.321824
  7. Gupta, V., Some approximation properties of q-Durrmeyer operators, Appl. Math. Comput., 197(1) (2008), 172-178. https://doi.org/10.1016/j.amc.2007.07.056
  8. Jing, S., The q-deformed binomial distribution and its asymptotic behaviour, J. Phys. A: Math. Gen., 27(2) (1994), 493-499. https://doi.org/10.1088/0305-4470/27/2/031
  9. Köroğlu, B., Taşdelen Yeşildal, F., On the eigenstructure of the (α, q)-Bernstein operator, Hacet. J. Math. Stat., 50(4) (2021), 1111-1122. https://doi.org/10.15672/hujms.779544
  10. Landau, L. D., Lifshitz, E. M., Mechanics: Course of Theoretical Physics, Vol. 1, 3rd edition, Butterworth-Heinemann, 1976.
  11. Landau, L. D., Lifshitz, E. M., Quantum Mechanics: Non-Relativistic Theory 3rd Edition, Vol. 3, Butterworth-Heinemann, 1981.
  12. Lupaş, A., A q-analogue of the Bernstein operator, University of Cluj-Napoca, Seminar on numerical and statistical calculus, 9 (1987), 85-92.
  13. Ostrovska, S., Turan, M., On the eigenvectors of the q-Bernstein operators, Math. Methods Appl. Sci., 37(4) (2014), 562-570. https://doi.org/10.1002/mma.2814
  14. Ostrovska, S., Turan, M., On the block functions generating the limit q-Lupaş operator, Quaest. Math., 46(4) (2023), 711-719. https://doi.org/10.2989/16073606.2022.2040632
  15. Phillips, G. M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4 (1997), 511-518.
  16. Rajagpoal, L., Roy, S. D., Design of maximally-flat FIR filters using the Bernstein polynomial, IEEE Trans. Circuits Syst., 34(12) (1987), 1587-1590. https://doi.org/10.1109/TCS.1987.1086077
  17. Stancu, D. D., Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20 (1983), 211-229. https://doi.org/10.1007/BF02575593
  18. Xiang, X., Stancu polynomials based on the q-integers, Anal. Theory Appl., 28(3) (2012), 232-241. https://doi.org/10.3969/j.issn.1672-4070.2012.03.003
  19. Yun, L., Xiang, X., On shape-preserving properties and simultaneous approximation of Stancu operator, Anal. Theory Appl., 24 (2008), 195-204. https://doi.org/10.1007/s10496-008-0195-0
  20. Yun, L., Wang, R., Approximation and shape-preserving properties of q-Stancu operator, Anal. Theory Appl., 27 (2011), 201-210. https://doi.org/10.1007/s10496-011-0201-9
  21. Zee, A., Quantum Field Theory in a Nutshell, 2nd Edition, Princeton University Press, Princeton, 2003.