Duality relations and characterizations of best approximation for p-convex sets

Ştefan Cobzaş; Ioan Muntean

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Ştefan Cobzaş "Babeş-Bolyai" University, Cluj-Napoca, Romania
Ioan Muntean "Babeş-Bolyai" University, Cluj-Napoca, Romania

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References

Aleman, Alexandru On some generalizations of convex sets and convex functions. Anal. Numér. Théor. Approx. 14 (1985), no. 1, pp. 1-6, MR0830509.

Asplund, Edgar Čebyšev sets in Hilbert space. Trans. Amer. Math. Soc. 144, 1969 pp. 235-240, MR0253023, https://doi.org/10.1090/s0002-9947-1969-0253023-7

Cholewa, Piotr W. Remarks on the stability of functional equations. Aequationes Math. 27 (1984), no. 1-2, pp. 76-86, MR0758860, https://doi.org/10.1007/bf02192660

Dunford, Nelson; Schwartz, Jacob T. Linear Operators. I. General Theory. With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7 Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London 1958 xiv+858 pp., MR0117523.

Fischer, Pal; Słodkowski, Zbigniew Christensen zero sets and measurable convex functions. Proc. Amer. Math. Soc. 79 (1980), no. 3, pp. 449-453, MR0567990, https://doi.org/10.1090/s0002-9939-1980-0567990-5

Franchetti, C.; Singer, I. Best approximation by elements of caverns in normed linear spaces. Boll. Un. Mat. Ital. B (5) 17 (1980), no. 1, pp. 33-43, MR0572587.

Garkavi, A. L. Duality theorems for approximation by elements of convex sets. (Russian) Uspehi Mat. Nauk 16 1961 no. 4 (100), pp. 141-145, MR0132992.

Green, J. W.; Gustin, W. Quasiconvex sets. Canadian J. Math. 2, (1950). pp. 489-507, MR0042142, https://doi.org/10.4153/cjm-1950-046-x

Holmes, Richard B. Geometric functional analysis and its applications. Graduate Texts in Mathematics, No. 24. Springer-Verlag, New York-Heidelberg, 1975. x+246 pp., MR0410335, https://doi.org/10.1007/978-1-4684-9369-6

Klee, Victor Convexity of Chevyshev sets. Math. Ann. 142 1960/1961, pp. 292-304, MR0121633.

Klee, V., Remarks on nearest points in normed linear spaces. Proc. Colloq. Convexity (Copehagen 1965), pp. 168-176, Copenhagen, 1966.

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 Russian), Naukova Dumka, Kiev, 1982.

Muntean, Ioan Support points of p-convex sets. Proceedings of the colloquium on approximation and optimization (Cluj-Napoca, 1985), pp. 293-302, Univ. Cluj-Napoca, Cluj-Napoca, 1985, MR0847281.

Muntean, Ioan A multiplier rule in p-convex programming. Seminar on mathematical analysis (Cluj-Napoca, 1985), pp. 149-156, Preprint, 85-7, Univ. "Babeş-Bolyai", Cluj-Napoca, 1985, MR0833779.

von Neumann, John, On complete topological spaces. Trans. Amer. Math. Soc. 37 (1935), no. 1, pp. 1-20, MR1501776, https://doi.org/10.1090/s0002-9947-1935-1501776-7

Pumplin, D., The Hahn-Banach theorem for totally convex spaces. Demonstratio Math., 18 (1985), pp. 567-588.

Rubinshteĭn, G. Sh., Dual extremum problems (in Russian), Dokl. Akad. Nauk SSSR, 152 (1963), pp. 288-291.

Schaefer, Helmut H. Topological vector spaces. The Macmillan Co., New York; Collier-Macmillan Ltd., London 1966 ix+294 pp., MR0193469.

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

Thibault, Lionel Continuity of measurable convex and biconvex operators. Proc. Amer. Math. Soc. 90 (1984), no. 2, pp. 281-284, MR0727250, https://doi.org/10.1090/s0002-9939-1984-0727250-x

Toader, Gheorghe Some generalizations of the convexity. Proceedings of the colloquium on approximation and optimization (Cluj-Napoca, 1985), pp. 329-338, Univ. Cluj-Napoca, Cluj-Napoca, 1985, MR0847286.