Korovkin theorem in modular spaces

• Autorzy: Bardaro C. , Mantellini I.
• Języki publikacji: EN

Abstrakty

EN

In this paper we obtain an extension of the classical Korovkin theorem in abstract modular spaces. Applications to some discrete and integral operators are discussed.

Słowa kluczowe

EN

modular space; linear operator; Korovkin theorem; moments

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2007
• Tom: Vol. 47, [Z] 2
• Strony: 239--253
• Opis fizyczny: bibliogr. 26 poz.

Twórcy

autor

Bardaro C.

autor

Mantellini I.

• Department of Mathematics and Informatics, University of Perugia Via Vanvitelli 1, 06123 Perugia, Italy URL: www.unipg.it/ bardaro,

Bibliografia

• [1] F. Altomare and M. Campiti, Korovkin-type approximation theory and its applications, Walter de Gruyter, Berlin, New York, 1994.
• [2] F. Barbieri, Approssimazione mediante nuclei momento, Atti Sem. Mat. Fis. Univ. Modena, 32, (1983), 308-328.
• [3] C. Bardaro, P.L. Butzer, R.L. Stens and G. Vinti, Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals, Analysis, 23, (2003), 299-340.
• [4] C. Bardaro and I. Mantellini, Approximation properties in abstract modular spaces for a class of general sampling type operators, Applicable Analysis, 85(4), (2006), 383-413.
• [5] C. Bardaro and I. Mantellini, Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math., 27(4), (2006), 431-447.
• [6] C. Bardaro and I. Mantellini, A Voronovskaya-type theorem for a general class of discrete operators, to appear in Rocky Mountain J. Math.
• [7] C. Bardaro, J. Musielak and G. Vinti, Nonlinear integral operators and applications, De Gruyter Series in Nonlinear Analysis and Appl.,Vol.9, 2003.
• [8] C. Bardaro and G. Vinti, Modular convergence in generalized Orlicz spaces for moment type operators, Applicable Analysis, 32, (1989), 265-276.
• [9] S.N. Bernstein, Demonstration du theoreme de Weierstrass fondee sur le calcul de probabilities, Com. of the Kharkov Math. Soc.,13, (1912), 1-2.
• [10] H. Bohman, On approximation of continuous and of analytic functions, Arkiv Math., 2(3), (1952), 43-56.
• [11] P.L. Butzer and R.J. Nessel, Fourier Analysis and Approximation I, Academic Press, New York-London, 1971.
• [12] R.A. DeVore, The approximation of continuous functions by positive linear operators, Lecture notes in Math., 293, Springer-Verlag, 1972.
• [13] R.A. DeVore and G. G. Lorentz, Constructive Approximation, Grund. Math. Wiss. 303, Springer Verlag, 1993.
• [14] K. Donner, Korovkin theorems in Lp-spaces, J. Funct. Anal., 42(1), (1981), 12-28.
• [15] S.M. Eisenberg, Korovkin's theorem, Bull. Malaysian Math. Soc., 2(2), (1979), 13-29.
• [16] M.W. Grossman, Note on a generalized Bohman-Korovkin theorem, J. Math. Anal. Appl.,45, (1974), 43-46.
• [17] P.P. Korovkin, On convergence of linear positive operators in the spaces of continuous functions, (Russian), Doklady Akad. Nauk. S.S.S.R.,90, (1953), 961-964.
• [18] P.P. Korovkin, Linear operators and approximation theory, Hindustan, Delhi, 1960.
• [19] W.M. Kozlowski, Modular Function Spaces, Pure Appl. Math., Marcel Dekker, New York and Basel, 1988.
• [20] G. G. Lorentz, Approximation of Functions, Chelsea Publ. Comp. New York, 1986.
• [21] I. Mantellini, Generalized sampling operators in modular spaces, Commentationes Math., 38, (1998), 77-92.
• [22] J. Musielak and W. Orlicz, On modular spaces, Studia Math., 18, (1959), 49-65.
• [23] J. Musielak, Orlicz Spaces and Modular Spaces, Springer-Verlag, Lecture Notes in Math., 1034 (1983).
• [24] J. Musielak, Nonlinear approximation in some modular function spaces I, Math. Japon., 38, (1993), 83-90.
• [25] P. Renaud, A Korovkin theorem for abstract Lebesgue spaces, J. Approx. Theory, 102, (2000), 13-20.
• [26] E. Schäfer, Korovkin's theorems: a unifying version, Functiones et Approximatio, 18, (1989), 43-49.