Finitely defined functionals and divided differences

Authors

  • Mircea Ivan Technical University of Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat332-773

Keywords:

divided difference, finitely defined functionals
Abstract views: 191

Abstract

We give a necessary and sufficient condition for representing finitely defined functionals in terms of divided differences. As particular cases we obtain formulas of Tiberiu Popoviciu, Newton, etc.

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References

DeVore, R. A. and Lorentz, G. G., Constructive Approximation, Springer Verlag, Berlin Heildelberg New York, 1993. DOI: https://doi.org/10.1007/978-3-662-02888-9

Kacsó, D. P., Approximation by means of piecewise linear functions, Results Math., 35 (1--2), pp. 89-102, 1999, https://doi.org/10.1007/BF03322024. DOI: https://doi.org/10.1007/BF03322024

Popoviciu, E., Mean value theorems and their connection to the interpolation theory, Editura Dacia, Cluj, 1972 (in Romanian).

Popoviciu, T., Introduction à la théorie des différences divisées, Bull. Math. de la Soc. Roumaine des Sci., 42 (1), pp. 65-78, 1940.

Popoviciu, T., Notes sur les fonctions convexes d'ordre supérieure (IX), Bull. Math. de la Soc. Roumaine des Sci., 43 (1-2), pp. 85-141, 1941.

Popoviciu, T., Curs de Analiză Matematică, Partea III-a, Continuitate, Babeş-Bolyai University Publishing House, Cluj-Napoca, 1974 (in Romanian).

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Published

2004-08-01

How to Cite

Ivan, M. (2004). Finitely defined functionals and divided differences. Rev. Anal. Numér. Théor. Approx., 33(2), 175–181. https://doi.org/10.33993/jnaat332-773

Issue

Vol. 33 No. 2 (2004)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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