On the Lamé point and its generalizations in a normed space
Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 267-286 Cet article a éte moissonné depuis la source Math-Net.Ru

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Existence and uniqueness conditions are investigated for an element $y^*$ which belongs to a subset $G$ of a normed linear space $E$ and minimizes the following functional over $G$: $$ F(y)=\int_A e(x-y)\,\mu(dx), $$ where $e(x)$ is a functional given on $E$ and bounded from below, $A$ is a Borel subset of $E$, and $\mu$ is a measure defined on the $\sigma$-algebra of the Borel subsets of $A$. Bibliography: 16 titles.
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     title = {On the {Lam\'e} point and its generalizations in a~normed space},
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A. L. Garkavi; V. A. Shmatkov. On the Lamé point and its generalizations in a normed space. Sbornik. Mathematics, Tome 24 (1974) no. 2, pp. 267-286. http://geodesic.mathdoc.fr/item/SM_1974_24_2_a4/

[1] S. Banach, C. Kuratovski, “Sur une généralisation du problème de la mesure”, Fundam. Math., 14 (1929), 127–131 | Zbl

[2] M. M. Vainberg, Variatsionnyi metod i metod monotonnykh operatorov, izd-vo «Nauka», Moskva, 1972 | MR

[3] A. L. Garkavi, “O nailuchshei seti i nailuchshem sechenii mnozhestva v normirovannom prostranstve”, Izv. AN SSSR, seriya matem., 26 (1962), 87–106 | MR

[4] E. G. Golshtein, Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya, izd-vo «Nauka», Moskva, 1971 | MR

[5] N. Danford, Dzh. T. Shvarts, Lineinye operatory, t. I, IL, Moskva, 1962

[6] D. Jackson, “A general class of problems in approximation”, Amer. J. Math., 46 (1924), 215–234 | DOI | MR | Zbl

[7] M. M. Dei, Normirovannye lineinye prostranstva, IL, Moskva, 1961

[8] M. P. Caroll, H. W. McLaughlin, “$L_1$ approximation of vector-valued functions”, J. Approxim. Theory, 7:2 (1973), 122–133 | DOI | MR

[9] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, izd-vo «Nauka», Moskva, 1968 | MR

[10] M. G. Krein, A. A. Nudelman, Problema momentov Markova i ekstremalnye zadachi, izd-vo «Nauka», Moskva, 1973 | MR

[11] S. F. Morozov, V. I. Plotnikov, “O neobkhodimykh i dostatochnykh usloviyakh nepreryvnosti i polunepreryvnosti funktsionalov variatsionnogo ischisleniya”, Matem. sbornik, 57 (99) (1962), 265–280 | MR | Zbl

[12] F. Ruston, “Conjugate Banach spaces”, Proc. Cambridge Phil. Soc., 53 (1957), 576–580 | DOI | MR | Zbl

[13] Yu. G. Reshetnyak, “Obschie teoremy o polunepreryvnosti i skhodimosti s funktsionalom”, Sib. matem. zh., 8:5 (1967), 1051–1067

[14] G. Sh. Rubinshtein, “Ob odnoi ekstremalnoi zadache v lineinom normirovannom prostranstve”, Sib. matem. zh., 6:3 (1965), 183–215

[15] W. Sierpinski, E. Szpilrajn, “Remarque sur le problème de la mesure”, Fundam. Math., 26 (1936), 253–261 | MR

[16] P. Khalmosh, Teoriya mery, IL, Moskva, 1953