On a theorem of V.N. Nikolski on characterization of best approximation for convex sets

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  • Ş. Cobzaş "Babeş-Bolyai" University, Cluj-Napoca, Romania
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References

Aleman, A., On some generalizations of convex sets and convex fucntions, Anal. Numer. Théor. Approx. 14 (1985), pp. 1-6.

Azizov, A. S., New criteria for the element of best approximation for convex sets (in russian), Doklady Akad. Nauk SSR 27(1984), pp. 615-618.

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Cobzas, S. and Muntean, I., Duality relations and characterizations of best approximation for p-convex sets. Anal. Numer. Théor. Approx. 16(1987), pp. 95-108.

Dunford, M. and Schwartz, J. T., Linear Operators, I Interscience Publ., New York, 1958.

Garkavi, A. L., Duality theorems for approximation by elements of convex sets (in russian), Uspekhi Mat. Nauk 16(1961), pp. 141-145.

Garkavi, A. L., On a criterion for best approximation, (in Russian) Siberian Mat., J., 5(1964), pp. 472-476.

Green, J. W. and Gustin, W., Quasi-convex sets, Anad. J. Math. 2 (1950n), pp. 480-507, https://doi.org/10.4153/cjm-1950-046-x

Korneĭchuk, N. P., Extremal Problems of Approximation Theory (in russian), Nauka, Moscow 1976.

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Nikolski, V. N., Extension of a theorem of A. N. Kolmogorov to Banach spaces (in Russian), Studies on the Contemporany Problems of Constructive Function Theory (red. V. I. Smirnov), Moscow 1961, pp. 335-337.

Nikloski, V. N., Best approximation by elements of convex sets in normed linear spaces (in Russian) Uch. Zap. Kalinin Gos. Ped. Inst. 29(1963), pp. 85-119.

Ponstein, J., Seven kinds of convexity, SIAM Rev. 9(1967), pp. 115-119,

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Singer, I., Choquet spaces and best approximation, Math. Ann. 148(1962), pp. 330-340, https://doi.org/10.1007/bf01451140

Singer, I., Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces. Springer-Verlag, Berlin - Heidelberg - New York and Editura Academiei Bucharest, 1970.

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Published

1990-02-01

How to Cite

Cobzaş, Ş. (1990). On a theorem of V.N. Nikolski on characterization of best approximation for convex sets. Anal. Numér. Théor. Approx., 19(1), 7–13. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/1990-vol19-no1-art2

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