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

On the Mellin-Gauss-Weierstrass operators in the Mellin-Lebesgue spaces

Fırat Özsaraç(KIRIKKALE UNIVERSITY)0000-0001-7170-9613
Pages
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Publication Date
2024-09-27
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Especially, we acquire the pointwise convergence of them at any Lebesgue point of a function $f$.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we present the modulus of smoothness of a function $f∈X_{c}^{p}$, which the Mellin-Lebesgue space, and later we state some properties of it.
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Key Findings & Data:In this way, the rate of convergence is gained.
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Conclusion & Impact:Especially, we acquire the pointwise convergence of them at any Lebesgue point of a function $f$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Mellin-Gauss-Weierstrass operators · Mellin-Lebesgue spaces · modulus of smoothness

Abstract

In this paper, we present the modulus of smoothness of a function $f∈X_{c}^{p}$, which the Mellin-Lebesgue space, and later we state some properties of it. In this way, the rate of convergence is gained. Moreover, we elucidate some pointwise convergence results for the Mellin-Gauss-Weierstrass operators. Especially, we acquire the pointwise convergence of them at any Lebesgue point of a function $f$.

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Cite This Article

Özsaraç, F. (2024). On the Mellin-Gauss-Weierstrass operators in the Mellin-Lebesgue spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 73 Issue: 3. https://doi.org/10.31801/cfsuasmas.1455235

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References (18)

  1. Aral, A., On a new approach in the space of measurable functions, Constr. Math. Anal., 6(4) (2023), 237-248. https://doi.org/10.33205/cma.1381787
  2. Aral, A., Acar, T., Kursun, S., Generalized Kantorovich forms of exponential sampling series, Anal. Math. Phys., 12(2) (2022), 1-19. https://doi.org/10.1007/s13324-022-00667-9
  3. Aral, A., Gupta, V., On the q analogue of Stancu-Beta operators, Applied Mathematics Letters, 25(1) (2012), 67-71. https://doi.org/10.1016/j.aml.2011.07.009
  4. Bardaro, C., Mantellini, I., Approximation properties for linear combinations of moment type operators, Comput. Math. Appl., 62(5) (2011), 2304–2313. https://doi.org/10.1016/j.camwa.2011.07.017
  5. Bardaro, C., Mantellini, I., Asymptotic behaviour of Mellin–Fejer convolution operators, East J. Approx., 17(2) (2011), 181–201. https://hdl.handle.net/11391/487296
  6. Bardaro, C., Mantellini, I., Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces, Mathematical Foundations of Computing, 5(3) (2022), 219-229. https://doi.org/10.3934/mfc.2021031
  7. Bardaro, C., Mantellini, I., On Mellin convolution operators: a direct approach to the asymptotic formulae, Integral Transf. Spec. Funct., 25(3) (2014), 182–195. https://doi.org/10.1080/10652469.2013.838755
  8. Bardaro, C., Mantellini, I., On the iterates of Mellin–Fejer convolution operators, Acta Appl. Math., 121(1) (2012), 213–229. https://doi.org/10.1007/s10440-012-9704-4
  9. Bardaro, C., Mantellini, I., Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math., 27(4) (2006), 431–447. https://api.semanticscholar.org/CorpusID:125122093
  10. Bardaro, C., Mantellini, I., Schmeisser, G., Exponential sampling series: convergence in Mellin-Lebesgue spaces, Results Math., 74 (2019), 1-20. https://doi.org/10.1007/s00025-019-1044-5
  11. Bardaro, C., Mantellini, I., Tittarelli, I., Convergence of semi-discrete exponential sampling operators in Mellin–Lebesgue spaces, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117 (2023), 1-15. https://doi.org/10.1007/s13398-022-01367-6
  12. Bardaro, C., Musielak J., Vinti, G., Nonlinear Integral Operators and Applications, De Gruyter Series in Nonlinear Analysis and Applications, New York, Berlin, 2003.
  13. Butzer, P. L., Jansche, S., A direct approach to the Mellin transform, J. Fourier Anal. Appl., 3(4) (1997), 325–376. https://doi.org/10.1007/BF02649101
  14. Butzer, P. L., Jansche, S., The exponential sampling theorem of signal analysis, Atti Semin. Mat. Fis. Univ. Modena, 46 (1998), 99–122. https://publications.rwthaachen.de/record/135935
  15. Butzer, P. L., Nessel, R. J., Fourier Analysis and Approximation I, Academic Press, New York-London, 1971.
  16. Gupta, V., Aral, A., Ozsarac, F., On semi-exponential Gauss-Weierstrass operators, Anal. Math. Phys., 12, 111 (2022). https://doi.org/10.1007/s13324-022-00723-4
  17. Kolbe, W., Nessel, R. J., Saturation theory in connection with Mellin transform methods, SIAM J. Math Anal., 3 (1972), 246-262. https://doi.org/10.1137/0503024
  18. Mamedov, R., The Mellin Transform and Approximation Theory, Elm, Baku, 1991.