Abstract
In this note we continue our previous investigations on the global approximation by Szász-Mirakjan operators. This time the functions to be approximated are in fact allowed to have exponential growth at infinity. The main point will be the derivation of the inverse theorem for the nonsaturated cases 0<α<2.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Becker, M., Umkehrsätze für positive lineare Operatoren, Dissertation, RWTH Aachen 1977.
Becker, M., An elementary proof of the inverse theorem for Bernstein polynomials . Aequationes Math, (in print).
Becker, M., Global approximation theorems for Szász-Mirakjan and Baskakov operators in polynomial weight spaces. Indiana Univ. Math. J. (in print).
Becker, M., Inverse theorems for Favard operators in weighted spaces.(to appear).
Becker, M..- Butzer, P.L. - Nessel, R.J., Saturation for Favard operators in weighted function spaces. Studia Math. 59 (1976), 33–47.
Becker, M. - Nessel, R.J., Iteration von Operatoren und Saturation in lokal konvexen Räumen . Forschungsberichte des Landes Nordrhein-Westfalen Nr. 2470, Westdeutscher Verlag Opladen, 1975, 27–49.
Becker, M. -Nessel, R.J., An elementary approach to inverse approximation theorems. J. Approximation Theory (in print).
Becker, M. - Nessel, R.J., Inverse results via smoothing. Proceedings International Conference on Constructive Function Theory, Blagoevgrad, 30.5.–5.6.1977, Sofia 1978 (in print).
Berens, H. - Lorentz, G.G., Inverse theorems for Bernstein polynomials. Indiana Univ. Math. J. 21 (1972), 693–708.
Butzer, P.L. -Scherer, K., Jackson and Bernstein-type inequalities for families of commutative operators in Banach spaces. J. Approximation Theory 5 (1972), 308–342.
Ditzian, Z., Convergence of sequences of linear positive operators: Remarks and applications. J. Approximation Theory 14 (1975), 296–301.
Grundmann, A., Personal communication to Dr. E. Stark. July 1975.
Kemper, J. -Nessel, R.J., Gewichtete Approximation durch variations-vermindernde Operatoren vom Faltungstyp . Forschungsberichte des Landes Nordrhein-Westfalen Nr. 2311, Westdeutscher Verlag Opladen, 1973, 1–49.
Kucharski, D., Approximationssätze für Szász-Mirakjan, Baskakov — und Favard-Operatoren in gewichteten Räumen. Diplomarbeit, RWTH Aachen 1977.
Lorentz, G.G., Inequalities and the saturation classes of Bernstein polynomials . in: On Approximation Theory, ed. P.L. Butzer - J. Korevaar, Proc. Oberwolfach, ISNM 5, Birkhäuser Verlag, Basel 1964, 200–207.
Martini, R., On the approximation of functions together with their derivatives by certain linear positive operators . Indag. Math. 31 (1969), 473–481.
May, C.P., Saturation and inverse theorems for combinations of a class of exponential-type operators . Canad. J. Math. 28 (1976), 1224–1250.
Micchelli, C.A., Saturation classes and iterates of operators. Dissertation, Stanford 1969.
Mirakjan, G.M., Approximation of continuous functions with the aid of polynomials ... . Dokl. Akad. Nauk SSSR 31 (1941), 201–205.
Szász, O., Generalization of S. Bernstein’s polynomials to the infinite interval. J. Res. Nat. Bur. Standards Sect. B. 45 (1950), 239–245.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Birkhäuser Verlag Basel
About this chapter
Cite this chapter
Becker, M., Kucharski, D., Nessel, R.J. (1978). Global Approximation Theorems for the Szász-Mirakjan Operators in Exponential Weight Spaces. In: Butzer, P.L., Szökefalvi-Nagy, B. (eds) Linear Spaces and Approximation / Lineare Räume und Approximation. International Series of Numerical Mathematics / Intermationale Schriftenreihe zur Numberischen Mathematik / Sùrie Internationale D’analyse Numùruque, vol 40. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7180-8_28
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7180-8_28
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-0979-4
Online ISBN: 978-3-0348-7180-8
eBook Packages: Springer Book Archive