Abstract
The aim of this work is to present some density theorems and a Bishop type theorem in the set C(X; [0, 1]) of continuous functions with values in the unit interval.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bishop, E.: A generalization of the Stone–Weierstrass theorem. Pac. J. Math. 11, 777–783 (1961)
Brosowski, B., Deutsch, F.: An elementary proof of the Stone–Weierstrass theorem. Proc. Am. Math. Soc. 81, 89–92 (1981)
Bucur, I.: A version of Stone–Weierstrass theorem based on a Gavriil Paltineanu result in approximatiom theory. In: Proceedings of the Mathematical and Educcational Symposium of Department of Mathematics and Computer Science, pp. 3–7. UTCB (2014)
Jewett, R.I.: A variation on the Stone–Weierstrass theorem. Proc. Am. Math. Soc. 14, 690–693 (1963)
Machado, S.: On Bishop’s generalization of the Stone–Weierstrass theorem. Indag. Math. 39, 218–224 (1977)
Paltineanu, G.: Some applications of Bernoulli’s inequality in the approximation theory. Rom. J. Math. Comput. Sci. 4(1), 1–11 (2014)
Prolla, J.B.: A generalized Berstein approximation theorem. Math. Proc. Camb. Philos. Soc. 104, 317–330 (1988)
Prolla, J.B.: On Von Neumann’s variation of the Weierstrass–Stone theorem. Numer. Funct. Anal. Optim. 13(3–4), 349–353 (1992)
Ransford, T.J.: A short elementary proof of Bishop–Stone–Weierstrass theorem. Math. Proc. Camb. Philos. Soc. 96, 309–311 (1984)
Výborný, V.: The Weierstrass theorem on polynomial approximation. Mathematica Bohemica 130(2), 161–165 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Paltineanu, G., Bucur, I. Some Density Theorems in the Set of Continuous Functions with Values in the Unit Interval. Mediterr. J. Math. 14, 44 (2017). https://doi.org/10.1007/s00009-017-0870-5
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00009-017-0870-5