PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On the order of BVφ - approximation of convolution integrals over the line group

Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Here we study the rate of BVφ - approximation of higher order for a class of linear integral operators of convolution type over the line group.
Twórcy
autor
  • Universitá degli Studi di Perugia, Dipartimento di Matematica e Informatica, Via Vanvitelli, 1, 06123 Perugia - Italia
autor
  • Universitá degli Studi di Perugia, Dipartimento di Matematica e Informatica, Via Vanvitelli, 1, 06123 Perugia - Italia
Bibliografia
  • [1] J. A. Adeli and J. de la Cal, Bemstein-type operators diminish the φ-variation, Constr. Approx. 12 (1986), 489-507.
  • [2] F. Barbieri, Approssimazione mediante nuclei momento, Atti Sem. Mat. Fis. Univ. Modena 32 (1983), 308-328.
  • [3] C. Bardaro, On approximation properties for some classes of linear operators of convolution type, Atti Sem. Mat. Fis. Univ. Modena 33 (1984), 329-356.
  • [4] C. Bardaro, P. L. Butzer, R. L. Stens and G. Vinti, Convergence in variation and rates of approximation for Bernstein type polynomials and singular integrals, Analysis (Münich) 23 (4), (2003), 299-346.
  • [5] C. Bardaro, J. Musielak and G. Vinti, Nonlinear Integral Operators and Applications, de Gruyter Series in Nonlinear Analysis and Applications, vol. 9, W. De Gruyter, Berlin - New York, 2003.
  • [6] C. Bardaro, S. Sciamannini and G. Vinti, Convergence in BVφ by nonlinear Mellin-type convolution operators, Funct. Approx. Comment. Math. 29 (2001), 17-28.
  • [7] C. Bardaro and G. Vinti, On convergence of moment operators with respect to φ-variation, Appl. Anal. 41 (1991), 247-256.
  • [8] C. Bardaro and G. Vinti, Some estimates of integral operators with respect to the multidimensional Vitali φ-variation and applications in fractional calculus, Rend. Mat., Serie VII 11 (1991), 405-416.
  • [9] D. Bugajewska, D. Bugajewski and H. Hudzik, BVφ-solutions of non-linear integral eguations, to appear, 2003.
  • [10] P. L. Butzer and R. J. Nessel, Fourier Analysis and Approximation, I, Academic Press, New York-London, 1971.
  • [11] J. Ciemnoczołowski and W. Matuszewska, Some properties of functions of bounded φ-variation and of bounded φ-variation in the sense of Wiener, Bull. Polish Sci. Math. 35 (1987), 185-194.
  • [12] E. Cohen, On the degree of approximation of a function by the partial sums of its Fourier series, Trans. Amer. Math. Soc 235 (1978), 35-74.
  • [13] E. Cohen, On the Fourier coefficients and continuity of functions of class V*φ, Rocky Mountains J. Math. 9 (1979), 227-237.
  • [14] V. V. Cristyakov and O. E. Galkin, Mappings of bounded Φ-variation with arbitrary function Φ, Journal of Dynamical and Control Systems 4 (2) (1998), 217-247.
  • [15] S. Gniłka, On the generalized Helly’s Theorem, Funct. Approx. Comment. Math. 4 (1976), 109-112.
  • [16] K. Hoffman, Analysis in Euclidean Spaces, Prentice-Hall Inc. Englewood Cliffs, N.J., 1975.
  • [17] R. Leśniewicz and W. Orlicz, On generalized variations II, Studia Math. 45 (1973), 71-109.
  • [18] I. Mantellini and G. Vinti, Φ-variation and nonlinear integral operators, Atti Sem. Mat. Fis. Univ. Modena, a special issue of the International Conference in Honour of Professor Calogero Vinti, Suppl. Vol 46 (1998), 847-862.
  • [19] J. Musielak, Orlicz Spaces and Modular Spaces, Springer-Verlag, Lecture Notes in Math., 1034, 1983.
  • [20] J. Musielak and W. Orlicz, On spaces of functions of finite generalized variation, Bull. Acad. Pol. Sci. Cl. III. 5 (1957), 389-392.
  • [21] J. Musielak and W. Orlicz, On generalized variation I, Studia Math. 18 (1959), 11-41.
  • [22] F. Prus-Wiśniowski, On superposition of functions of bounded φ-variation, Proc. Amer. Math. Soc. 107 (1989), 361-366.
  • [23] A. R. K. Ramanazov, On approximation of functions in terms of Φ-variation, Analysis Mathematica 20 (1994), 263-281.
  • [24] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Monograph Textbooks Pure Appl. Math, Marcel Dekker Inc., New York, 1991.
  • [25] S. Sciamannini and G. Vinti, Convergence and rate of approximation in BVφ for a class of integral operators, Approximation Theory and its Applications 17: 4 (2001), 17-35.
  • [26] S. Sciamannini and G. Vinti, Convergence results in BVφ for a class of nonlinear Volterra-Hammerstein integral operators and applications, Journal of Concrete and Applicable Mathematics 1 (2003), 315-334.
  • [27] J. Szelmeczka, On convergence of singular integrals in the generalized variation metric, Funct. Approx. Comment. Math. 15 (1986), 53-58.
  • [28] C. Vinti, Perimetro - Variazione, Annali Scuola Norm. Sup. Pisa, serie III 43 (1964), 201-231.
  • [29] C. Vinti, Sull’approssimazione in perimetro e in area, Atti Sem. Mat. Fis. Univ. Modena 13 (1964), 187-197.
  • [30] G. Vinti, Generalized φ-variation in the sense of Vitali: estimates for integral operators and applications in fractional calculus, Comment. Math. Prace Matem. 34 (1994), 199-213.
  • [31] V. Zanelli, Funzioni momento convergenti dal basso in variazione di ordine non intero, Atti Sem. Mat. Fis. Univ. Modena 30 (1981), 355-369.
Uwagi
Dedicated to Professor J. Musielak, on the occasion of the 75th anniversary of his birthday, with profound esteem and sincere friendship.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0007-0047
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.