PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Convergence of generalized sampling series in weighted spaces

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present paper deals with an extension of approximation properties of generalized sampling series to weighted spaces of functions. A pointwise and uniform convergence theorem for the series is proved for functions belonging to weighted spaces. A rate of convergence by means of weighted moduli of continuity is presented and a quantitative Voronovskaja-type theorem is obtained.
Wydawca
Rocznik
Strony
153--162
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • Department of Mathematics, Selcuk University, Faculty of Science, Selcuklu, 42003, Konya, Turkey
  • Department of Mathematics, Bilecik Seyh Edebali University, Faculty of Science, Bilecik, Turkey,
autor
  • Department of Mathematics, Kirikkale University, Faculty of Science and Arts, Yahsihan, 71450, Kirikkale, Turkey
  • Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy
autor
  • Department of Mathematics, Selcuk University, Faculty of Science, Selcuklu, 42003, Konya, Turkey
  • Department of Mathematics and Computer Science, University of Perugia, 1, Via Vanvitelli, 06123 Perugia, Italy
Bibliografia
  • [1] P. L. Butzer and W. Splettstosser, A sampling theorem for duration limited functions with error estimates, Inform. Contr. 34 (1977), 55–65.
  • [2] S. Ries and R. L. Stens, Approximation by generalized sampling series, Proceedings of the International Conference on Constructive Theory of Functions (Varna, 1984), Bulgarian Academy of Science, Sofia, 1984, 764–756.
  • [3] W. Splettstosser, On generalized sampling sums based on convolution integrals, Arch. Elek. Ubertr. 32 (1978), 267–275.
  • [4] H. Feichtinger and K. Gröchenig, Theory and practice of irregular sampling, in: J. Benedetto, M. Frazier (Eds.), Wavelets: Mathematics and Applications, CRC Press Inc., London, 1994, pp. 305–363.
  • [5] K. Gröchenig, Reconstruction algorithms in irregular sampling, Math. Comp. 59 (1992), 181–194.
  • [6] P. L. Butzer and R. L. Stens, Linear prediction by samples from the past, in: Advanced Topics in Shannon Sampling and Interpolation Theory, Springer, New York, 1993, pp. 157–183.
  • [7] S. N. Bernstein, Démonstration du théorème de Weierstrass fondée sur la calcul des probabilités, Comm. Soc. Math. Charkow Sér. 13 (1912), no. 2, 1–2.
  • [8] V. A. Baskakov, An example of a sequence of linear positive operators in space of continuous functions, Dokl. Akad. Nauk. SSSR 113 (1957), 249–251. (in Russian)
  • [9] G. G. Lorentz, Bernstein Polynomials, 2nd edition, Chelsea Publishing Company, New York, 1986.
  • [10] H. Bohman, On approximation of continuous and analytic functions, Ark. Mat. 2 (1952), 43–56.
  • [11] P. P. Korovkin, On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR 90 (1953), 961–964.
  • [12] A. D. Gadziev, The convergence problem for a sequence of positive linear operators on unbounded sets, and Theorems analogous to that of P. P. Korovkin, Dokl. Akad. Nauk SSSR 218 (1974), no. 5, 1001–1004.
  • [13] A. D. Gadjiev, On P. P. Korovkin-type theorems, Mat. Zametki 20 (1976), no. 5, 781–786.
  • [14] T. Acar, A. Aral, and I. Raşa, The new forms of Voronovskaya’s theorem in weighted spaces, Positivity 20 (2016), no. 1, 25–40.
  • [15] T. Acar, M. C. Montano, P. Garrancho, and V. Leonessa, On Bernstein-Chlodovsky operators preserving e x−2 , Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 5, 681–698.
  • [16] T. Acar, M. C. Montano, P. Garrancho, and V. Leonessa, Voronovskaya type results for Bernstein-Chlodovsky operators preserving e x−2 , J. Math. Anal. Appl. 491 (2020), no. 1, 124307.
  • [17] C. Bardaro, J. Musielak, and G. Vinti, Nonlinear integral operators and applications, De Gruyter Series in Nonlinear Analysis and Applications 9, De Gruyter, New York-Berlin, 2003.
  • [18] S. Nanda, P. K. Dash, T. Chakravorti, and S. Hasan, A quadratic polynomial signal model and fuzzy adaptive filter for frequency and parameter estimation of nonstationary power signals, Measurement 87 (2016), 274–293.
  • [19] 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 (2007), no. 1, 29–52.
  • [20] D. Costarelli and G. Vinti, Rate of approximation for multivariate sampling Kantorovich operators on some functions spaces, J. Integral Equations Appl. 26 (2014), no. 4, 455–481.
  • [21] A. Holhos, Quantitative estimates for positive linear operators in weighted spaces, Gen. Math. 16 (2008), no. 4, 99–104.
  • [22] N. Ispir, On modified Baskakov operators on weighted spaces, Turkish J. Math. 26 (2001), no. 3, 355–365.
  • [23] D. Costarelli and G. Vinti, Order of approximation for sampling Kantorovich operators, J. Integral Equ. Appl. 26 (2014), no. 3, 345–368.
  • [24] D. Costarelli and G. Vinti, An inverse result of approximation by sampling Kantorovich series, Proc. Edinb. Math. Soc. 62 (2019), no. 1, 265–280.
  • [25] D. Costarelli and G. Vinti, Inverse results of approximation and the saturation order for the sampling Kantorovich series, J. Approx. Theory 242 (2019), 64–82.
  • [26] D. Costarelli and G. Vinti, Saturation by the Fourier transform method for the sampling Kantorovich series based on bandlimited kernels, Anal. Math. Phys. 9 (2019), 2263–2280.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d33af84c-1cc9-4e26-a98b-e4f2bd9345df
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.