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Original Articles

Quantitative Approximation Properties for Iterates of Moment Operator

, &
Pages 261-272 | Received 23 Jun 2014, Published online: 30 Mar 2015

References

  • G.A. Anastassiou and S.G. Gal. Approximation Theory. Moduli of Continuity and Global Smoothness Preservation. Birkhäuser Boston, Inc., Boston, 2000.
  • L. Angeloni. A characterization of a modulus of smoothness in multidimensional setting. Boll. Unione Mat. Ital., 4(1):79–108, 2011.
  • L. Angeloni and G. Vinti. Approximation in variation by homothetic operators in multidimensional setting. Differential Integral Equations, 26(5–6):655–674, 2013.
  • F. Barbieri. Approximation by moment kernels. Atti Sem. Mat. Fis. Univ. Modena, 32(2):308–328, 1983.
  • C. Bardaro, P.L. Butzer and I. Mantellini. The foundations of the fractional calculus in Mellin transform setting with applications. J. Fourier Anal. Appl., 2015. To appear
  • C. Bardaro and I. Mantellini. Linear integral operators with homogeneous kernel: approximation properties in modular spaces. Applications to Mellin-type convolution operators and to some classes of fractional operators. In G.A. Anastassiou(Ed.), Applied Mathematics Reviews, volume 1, pp. 45–67. World Scientific Publ., River Edge, NJ, 2000. http://dx.doi.org/10.1142/9789812792686_0003.
  • C. Bardaro and I. Mantellini. Voronovskaya-type estimates for Mellin convolution operators. Results Math., 50(1–2):1–16, 2007. http://dx.doi.org/10.1007/s00025-006-0231-3.
  • C. Bardaro and I. Mantellini. A quantitative Voronovskaja formula for Mellin convolution operators. Mediterr. J. Math., 7(4):483–501, 2010. http://dx.doi.org/10.1007/s00009-010-0062-z.
  • C. Bardaro and I. Mantellini. Approximation properties for linear combinations of moment type operators. Comput. Math. Appl., 62:2304–2313, 2011. http://dx.doi.org/10.1016/j.camwa.2011.07.017.
  • C. Bardaro and I. Mantellini. A note on the Voronovskaja theorem for Mellin– Fejer convolution operators. Appl. Math. Lett., 24:2064–2067, 2011. http://dx.doi.org/10.1016/j.aml.2011.05.043.
  • C. Bardaro and I. Mantellini. On the iterates of Mellin–Fejer convolution operators. Acta Appl. Math., 121:213–229, 2012. http://dx.doi.org/10.1007/s10440-012-9704-4.
  • C. Bardaro and I. Mantellini. On Mellin convolution operators: a direct approach to the asymptotic formulae. Integral Transforms Spec. Funct., 25(3):182–195, 2014. http://dx.doi.org/10.1080/10652469.2013.838755.
  • C. Bardaro and G. Vinti. Modular convergence in generalized Orlicz spaces for moment type operators. Appl. Anal., 32:265–276, 1989. http://dx.doi.org/10.1080/00036818908839853.
  • A. Boccuto, D. Candeloro and A. Sambucini. Vitali-type theorems for filter convergence related to Riesz space-valued modulars and applications to stochastic processes. J. Math. Anal. Appl., 419(2):818–838, 2014. http://dx.doi.org/10.1016/j.jmaa.2014.05.014.
  • P.L. Butzer and H. Berens. Semi-Groups of Operators and Approximation. Springer-Verlag, Berlin, Heidelberg, New York, 1967.
  • P.L. Butzer and S. Jansche. A direct approach to the Mellin transform. J. Fourier Anal. Appl., 3:325–375, 1997. http://dx.doi.org/10.1007/BF02649101.
  • P.L. Butzer, A.A. Kilbas and J.J. Trujillo. Fractional calculus in the Mellin setting and Hadamard-type fractional integral. J. Math. Anal. Appl., 269:1–27, 2002. http://dx.doi.org/10.1016/S0022-247X(02)00001-X.
  • D. Candeloro and A.R. Sambucini. Filter convergence and decompositions for vector lattice-valued measures. Mediterr. J. Math., 2014. http://dx.doi.org/10.1007/s00009-014-0431-0.
  • R.A. DeVore and G.G. Lorentz. Constructive Approximation. Springer-Verlag, Berlin, Heidelberg, 1993.
  • C. Fiocchi. Variazione di ordine α e dimensione di Hausdorff degli insiemi di Cantor. Atti Sem. Mat. Fis. Univ. Modena, 34(2):649–667, 1991.
  • H. Gonska, P. Pitul and I. Rasa. On Peano's form of the Taylor remainder, Voronovskaja's theorem and the commutator of positive linear operators. In O. Agratini and P. Blaga(Eds.), Inter. Conf. Numerical Analysis and Approximation Theory, pp. 55–80, Cluj-Napoca, Romania, 2006.
  • J. Hadamard. Essai sur l'etude des fonctions donnees par leur developpement de Taylor. J. Math. Pures Appl., 8:101–186, 1892.
  • A.A. Kilbas, H.M. Srivastava and J.J. Trujillo. Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
  • L. Maligranda. Interpolation spaces in the theory of approximation. In Methods of Functional Analysis in Approximation Theory, volume 2, pp. 263–279, ISNM 76, Bombay, 1985, 1986. Birkhäuser.
  • R.G. Mamedov. The Mellin Transform and Approximation Theory. Elm, Baku, 1991. (in Russian)
  • J. Peetre. Exact interpolation theorems for Lipschitz continuous functions. Ricerche Mat., 18:239–259, 1969.
  • F. Ventriglia and G. Vinti. Nonlinear Kantorovich-type operators: a unified approach. Comm. Appl. Nonlinear Anal., 21(2):45–74, 2014.
  • C. Vinti. Sull'approssimazione in perimetro e in area. Atti Sem. Mat. Fis. Univ. Modena, 13:187–197, 1964.
  • G. Vinti. A general approximation result for nonlinear integral operators and applications to signal processing. Appl. Anal., 79:217–238, 2001. http://dx.doi.org/10.1080/00036810108840958.
  • G. Vinti and L. Zampogni. A unifying approach to convergence of linear sampling type operators in Orlicz spaces. Adv. Differential Equations, 16:573–600, 2011.
  • V. Zanelli. Funzioni momento convergenti dal basso in variazione di ordine non intero. Atti Sem. Mat. Fis. Univ. Modena, 30:355–369, 1981.

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