| Title:
|
Differentiability of convex functionals and boundedness of nonlinear operators and functionals (English) |
| Author:
|
Kolomý, Josef |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
10 |
| Issue:
|
1 |
| Year:
|
1969 |
| Pages:
|
91-114 |
| . |
| Category:
|
math |
| . |
| MSC:
|
46-45 |
| MSC:
|
47Hxx |
| MSC:
|
49Axx |
| idZBL:
|
Zbl 0189.45001 |
| idMR:
|
MR0248522 |
| . |
| Date available:
|
2008-06-05T20:29:47Z |
| Last updated:
|
2012-04-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/105218 |
| . |
| Reference:
|
[1] J. KOLOMÝ: On the differentiability of operators and convex functionals.Comment. Math. Univ. Carolinae 9 (1968), 441-454. MR 0238077 |
| Reference:
|
[2] J. KOLOMÝ: Gradient maps and boundedness of Gâteaux differentials.Comment. Math. Univ. Carolinae 9 (1968), 613-625. MR 0247464 |
| Reference:
|
[3] J. DANEŠ J. KOLOMÝ: On the continuity and differentiability properties of convex functionals.Comment. Math. Univ. Carolinae 9 (1968), 329-350. MR 0239415 |
| Reference:
|
[4] M. M. VAJNBERG: Variacionnyje metody issledovanija nelinejnych operatorov.Moskva 1956. |
| Reference:
|
[5] J. KOLOMÝ: On the differentiability of mappings and convex functionals.Comment. Math. Univ. Carolinae 8 (1967), 735-752. A correction ibid 9 (1968), 197. MR 0243348 |
| Reference:
|
[6] L. E. DUBINS: On differentiation of series term-by-term.Am. Math. Monthly 67 (1960) 771-772. Zbl 0100.05502, MR 0123120 |
| Reference:
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[7] J. DIEUDONNÉ: Foundations of Modern Analysis.New York, London 1960. MR 0120319 |
| Reference:
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[8] A. D. MICHAL: Differential calculus in linear topological spaces.Proc. Nat. Acad. Sci. U. S. A. 24 (1938), 340-342. Zbl 0019.31101 |
| Reference:
|
[9] KY FAN: Sur quelques notions fondamentales de l'analyse générale.Journ. Math. Pures Appl. 21 (1942), 289-368. MR 0009088 |
| Reference:
|
[10] M. BALANSAT: La différential en les espacios métricas affines.Matem. Notae 9 (1949), 29-51; 19 (1964), 43-62. |
| Reference:
|
[11] M. BALANSAT: La différentielle d'Hadamard-Fréchet dans les espaces vectoriels topologiques.Compt. Rend. Acad. Sci. (Paris) 251 (1960), 2459-2461; 253 (1961), 1240-1242. |
| Reference:
|
[12] S. F. LONG de FOGLIO: La différentielle au sense d'Hadamard-Fréchet dans les espaces L vectoriels.Portug. Math. 19 (1960) No 3-4, 165-184. MR 0124760 |
| Reference:
|
[1З] V. I. AVERBUCH O. G. SMOLJANOV: Različnyje opredělenija proizvodnoj v linejnych topologičeskich prostranstvach.Usp. mat. nauk t. 23 (1968), vyp. 4 (142), 67-116. MR 0246118 |
| Reference:
|
[14] V. F. DEMJANOV A. M. RUBINOV: Približennyje metody rešenija ekstremalnych zadač.Izd. Leningr. univ. 1968. MR 0244823 |
| Reference:
|
[15] E. ASPLUND: Fréchet differentiability of convex functions.Acta Math. 121 (1968), 1-2, 30-47. Zbl 0162.17501, MR 0231199 |
| Reference:
|
[16] K. KURATOWSKIJ: Topologia I.(rus. perevod), Moskva 1966. |
| Reference:
|
[17] E. ČECH: Topological spaces.Rev. ed. Academia Praha 1966. |
| Reference:
|
[18] S. BANACH: Théorie des opérations linéaires.Monografje Matematyczne, Warazaw 1932. Zbl 0005.20901 |
| Reference:
|
[19] E. HILLE R. S. PHILLIPS: Functional analysis and semigroup.Am. Math. Soc. Providence 1957. MR 0089373 |
| Reference:
|
[20] J. KOLOMÝ: On the differentiability of mappings in functional spaces.Comment. Math. Univ. Carolinae 8 (1967), 315-329. MR 0212569 |
| Reference:
|
[21] E. ČECH: Point sets.(engl. transl.) Academia, Praha 1969. MR 0256344 |
| Reference:
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[22] S. MAZUR L. STERNBACH: Über die Borelschen Typen von linearen Mengen.Studia Math. 4 (1930), 48-53. |
| Reference:
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[23] M. KATĚTOV: O normovaných vektorových prostorech.Rozpravy II. tř. České akad. 53, č. 45 (1944), 1-27. MR 0024068 |
| Reference:
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[24] M. M. DAY: Normed linear spaces.Springer 1958. Zbl 0082.10603, MR 0094675 |
| Reference:
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[25] S. MAZUR W. ORLICZ: Grundlegende Eigenschaften der polynomischen Operationen I, II.Studia Math. Vol. 5 (1934), 50-68; 179-189. |
| Reference:
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[26] M. ZORN: Gâteaux differentiability and essential boundedness.Duke Math. J. 12 (1945), 579-583. Zbl 0061.25001, MR 0014596 |
| Reference:
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[27] S. YAMAMURO: A note on the boundedness property of non-linear operators.Yokohama Math. J. 10 (1962), 19-23. Zbl 0188.45602, MR 0155187 |
| Reference:
|
[28] J. KOLOMÝ: Remarks on nonlinear functionals.Comment. Math. Univ. Carolinae 9 (1968), 145-155. MR 0238076 |
| Reference:
|
[29] N. BOURBAKI: Topologičeskije vektornyje prostranstva.(ruskij perevod). Moskva 1956. |
| . |
