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Dergiler / Constructive Mathematical Analysis / 2026 / Volume: 4 Issue: 2

Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces

Laura Angelonı(University of Perugia)0000-0002-2214-6751
Nursel Çetin(Ankara University)0000-0003-3771-6523
Danilo Costarellı(University of Perugia)0000-0001-8834-8877
Anna Rita Sambucını(University of Perugia)0000-0003-0161-8729
Gianluca Vıntı(University of Perugia)0000-0002-9875-2790
Sayfa
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Yayın Tarihi
2021-06-01
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Yapay Zeka Hızlı Bakış & Çıkarımlar

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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces.
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Temel Bulgular & Veri:As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes.
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Sonuç & Katkı:In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Multivariate sampling Kantorovich operators · Orlicz spaces · modulus of smoothness

Abstract

In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.

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Bu Makaleye Atıf Yap

Angelonı, L., Çetin, N., Costarellı, D., Sambucını, A. R., Vıntı, G. (2021). Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces. Constructive Mathematical Analysis, Volume: 4 Issue: 2. https://doi.org/10.33205/cma.876890

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Kaynakça (35)

  1. T. Acar, D. Costarelli and G. Vinti: Linear prediction and simultaneous approximation by m-th order Kantorovich type sampling series, Banach J. Math. Anal., 14 (4) (2020), 1481-1508.
  2. F. Altomare, M. Campiti: Korovkin-type approximation theory and its applications, De Gruyter studies in Mathematics, (2011).
  3. F. Altomare, M. Cappelletti Montano and V. Leonessa: On a Generalization of Szász-Mirakjan-Kantorovich Operators, Results Math., 63 (2013), 837-863.
  4. F. Altomare, M. Cappelletti Montano, V. Leonessa and I. Rasa: A generalization of Kantorovich operators for convex compact subsets, Banach J. Math. Anal., 11 (3) (2017), 591-614.
  5. F. Altomare, M. Cappelletti Montano, V. Leonessa and I. Rasa: Elliptic differential operators and positive semigroups associated with generalized Kantorovich operators, J. Math. Anal. Appl., 458 (1) (2018), 153-173.
  6. L. Angeloni, D. Costarelli, M. Seracini, G. Vinti and L. Zampogni: Variation diminishing-type properties for multivariate sampling Kantorovich operators, Bollettino U.M.I., Special issue dedicated to Prof. Domenico Candeloro, 13 (4) (2020), 595-605.
  7. L. Angeloni, D. Costarelli and G. Vinti: A characterization of the convergence in variation for the generalized sampling series, Ann. Acad. Sci. Fenn. Math., 43 (2018), 755-767.
  8. L. Angeloni, D. Costarelli and G. Vinti: Convergence in variation for the multidimensional generalized sampling series and applications to smoothing for digital image processing, Ann. Acad. Sci. Fenn. Math., 45 (2020), 751-770.
  9. F. Asdrubali, G. Baldinelli, F. Bianchi, D. Costarelli, A. Rotili, M. Seracini and G. Vinti: Detection of thermal bridges from thermographic images by means of image processing approximation algorithms, Appl. Math. Comput., 317 (2018), 160-171.
  10. C. Bardaro, I. Mantellini: Voronovskaya formulae for Kantorovich type generalized sampling series, Int. J. Pure Appl. Math., 62 (3) (2010), 247-262.
  11. C. Bardaro, I. Mantellini: Asymptotic formulae for multivariate Kantorovich type generalized sampling series, Acta Math. Sinica (ES), 27 (7) (2011), 1247-1258.
  12. C. Bardaro, J. Musielak and G. Vinti: Nonlinear Integral Operators and Applications, in: de Gruyter Series in Nonlinear Analysis and Applications, vol. 9, Walter de Gruyter & Co., Berlin, (2003).
  13. C. Bardaro, P. L. Butzer, R. L. Stens and G. Vinti: Kantorovich-type generalized sampling series in the setting of Orlicz spaces, Sampl. Theory Signal Image Process., 6 (1) (2007), 29-52.
  14. M. Cantarini, D. Costarelli and G. Vinti: A solution of the problem of inverse approximation for the sampling Kantorovich operators in case of Lipschitz functions, Dolomites Res. Notes Approx. DRNA, 13 (2020), 30-35.
  15. N. Çetin, D. Costarelli and G. Vinti: Quantitative estimates for nonlinear sampling Kantorovich operators, arXiv 2102.08651 (2021).
  16. F. Cluni, D. Costarelli, V. Gusella and G. Vinti: Reliability increase of masonry characteristics estimation by sampling algorithm applied to thermographic digital images, Probabilist Eng. Mech., 60 (2020), 103022.
  17. L. Coroianu, S. G. Gal: Lp- approximation by truncated max-product sampling operators of Kantorovich-type based on Fejer kernel, J. Integral Equations Applications, 29 (2) (2017), 349-364.
  18. L. Coroianu, S. G. Gal: Approximation by truncated max-product operators of Kantorovich-type based on generalized (Φ, Ψ)-kernels, Math. Methods Appl. Sci., 41 (17) (2018), 7971-7984.
  19. L. Coroianu, S. G. Gal: Approximation by max-product operators of Kantorovich type, Stud. Univ. Babes-Bolyai Math., 64 (2) (2019), 207-223.
  20. D. Costarelli, M. Seracini and G. Vinti: A segmentation procedure of the pervious area of the aorta artery from CT images without contrast medium, Math. Methods Appl. Sci., 43 (2020), 114-133.
  21. D. Costarelli, M. Seracini and G. Vinti: A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods, Appl. Math. Comput., 374 (2020), 125046.
  22. D. Costarelli, A. R. Sambucini and G. Vinti: Convergence in Orlicz spaces by means of the multivariate max-product neural network operators of the Kantorovich type, Neural Comput. & Applic., 31 (9) (2019), 5069-5078.
  23. D. Costarelli, R. Spigler: How sharp is the Jensen inequality ?, J. Inequal. Appl., 2015:69 (2015) 1-10.
  24. D. Costarelli, G. Vinti: Approximation by Multivariate Generalized Sampling Kantorovich Operators in the Setting of Orlicz Spaces, Bollettino U.M.I., Special issue dedicated to Prof. Giovanni Prodi, 9 (4) (2011), 445-468.
  25. D. Costarelli, G. Vinti: A quantitative estimate for the sampling Kantorovich series in terms of the modulus of continuity in Orlicz spaces, Constr. Math. Anal., 2 (1) (2019), 8-14.
  26. D. Costarelli, G. Vinti: An inverse result of approximation by sampling Kantorovich series, Proc. Edinburgh Math. Soc., 62 (1) (2019), 265-280.
  27. D. Costarelli, G. Vinti: Inverse results of approximation and the saturation order for the sampling Kantorovich series, J. Approx. Theor., 242 (2019), 64-82.
  28. D. Costarelli, G. Vinti: Saturation by the Fourier transform method for the sampling Kantorovich series based on bandlimited kernels, Anal. Math. Phys., 9 (2019), 2263-2280.
  29. E. D’Aniello, M. Maiuriello: A survey on composition operators on some function spaces, Aequat. Math., (2020).
  30. A. Krivoshein, M. A. Skopina: Multivariate sampling-type approximation, Anal. Appl., 15 (4) (2017), 521-542.
  31. J. Musielak, W. Orlicz: On modular spaces, Studia Math., 28 (1959), 49-65.
  32. J. Musielak: Orlicz Spaces and Modular Spaces, in: Lecture Notes in Mathematics, vol. 1034, Springer-Verlag, Berlin, (1983).
  33. M. M. Rao, Z.D. Ren: Theory of Orlicz Spaces, Marcel Dekker Inc., Pure and Appl. Math., New York-Basel-Hong Kong, (1991).
  34. M. M. Rao, Z. D. Ren: Applications of Orlicz Spaces, Marcel Dekker Inc., Monographs and Textbooks in Pure and applied Mathematics, vol. 250, New York, (2002).
  35. G. Vinti, L. Zampogni: Approximation by means of nonlinear Kantorovich sampling type operators in Orlicz spaces, J. Approx. Theor., 161 (2009), 511-528.