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

Authors

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

Abstract

Not available.

Downloads

Download data is not yet available.

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.

Burov, V. N., Approximation with restrictions in normed linear spaces (in Russian), Ukrain. Mat. J. 15(1963), pp. 135-144.

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.

Korneĭchuk, N. P., Ligun, A. A. and Doronin, V. G., Approximation with Restrictions (in Ruĭsian) Naukova Dumka, Kiev 1982.

Muntean, I., Support points of p-convex sets, Proc. Colloq. Approx. and Optimization (Cluj-Napoca 1984).

Muntean, I., A multiple rule in p-convex programming, Seminar on Math. Anal., Univ. of Cluj-Napoca, Preprint Nr. 7 (1985), pp. 149-156.

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,

Rubinshteĭn, G. Sh., On an extremal problem in a normed linear space (in russian), Sibirskii Mat. J. 6 (1965), pp. 711-714.

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.

Downloads

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

Issue

Section

Articles