Literature cited
S. I. Zukhovitskii and S. B. Stechkin, “Approximation to abstract functions with values in Banach space,” Dokl. Akad. Nauk SSSR,106, No. 5, 773–776 (1956).
D. Distel', The Geometry of Banach Spaces [in Russian], selected chapters, Vishcha Shkola, Kiev (1980).
Yu. A. Shashkin, “Convex sets, extremal points and simplexes,” Itogi Nauki i Tekhniki Mat. Anal.,11, VINITI, Moscow (1973), pp. 5–50.
A. J. Lazar, “Spaces of affine continuous functions on simplexes,” Trans. Am. Math. Soc.,134, No. 3, 503–525 (1968).
I. Singer, “Caractérisation des elements de meilleure approximation dans un espace de Banach quelconque,” Acta Sci. Math.,17, Nos. 3–4, 181–189 (1956).
R. Phelps, Lectures on Schocke's Theorems [Russian translation], Mir, Moscow (1968).
G. Sh. Rubinshtein, “A method of studying convex sets,” Dokl. Akad. Nauk SSSR,102, No. 3, 451–454 (1955).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 36, No. 1, pp. 89–101, July, 1984.
In conclusion, the author thanks Yu. A. Shashkin for setting the problem and for his attention to this article.
Rights and permissions
About this article
Cite this article
Ustinov, G.M. Chebyshev subspaces of spaces of abstract affine functions. Mathematical Notes of the Academy of Sciences of the USSR 36, 537–543 (1984). https://doi.org/10.1007/BF01139555
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01139555