| Title:
|
Higher order differentiability of nonlinear operators on normed spaces. I. (English) |
| Author:
|
Nashed, Zuhair M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
10 |
| Issue:
|
3 |
| Year:
|
1969 |
| Pages:
|
509-533 |
| . |
| Category:
|
math |
| . |
| MSC:
|
47-80 |
| MSC:
|
47Hxx |
| MSC:
|
49Axx |
| idZBL:
|
Zbl 0194.44802 |
| idMR:
|
MR0261413 |
| . |
| Date available:
|
2008-06-05T20:31:07Z |
| Last updated:
|
2012-04-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/105248 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/105250 |
| . |
| Reference:
|
[1] M. Z. NASHED: On the representation and differentiability of operators.(to appear). Zbl 0249.46024, MR 0390766 |
| Reference:
|
[2] J. DIEUDONNÉ: Foundations of Modern Analysis.Academic Pres, New York, 1960. MR 0120319 |
| Reference:
|
[3] L. A. LJUSTERNIK, V. J. SOBOLEV: Elements of Functional Analysis.Ungar, New York, 1961. MR 0141967 |
| Reference:
|
[4] M. M. VAINBERG: Variational Methods for the Stady of Monlinear Operators.Holden - Day, San Francisco, 1964. |
| Reference:
|
[5] L. V. KANTOROVICH, G. P. AKHILOV: Functional Analysis in Normed Spaces.Pergamon Press, New York, 1964. |
| Reference:
|
[6] A. D. MICHAL: Le calcul differentiel dans les espaces de Banach.vol. 1, 2. Gauthier - Villars, Paris, 1958, 1964. Zbl 0083.10901 |
| Reference:
|
[7] M. Z. NASHED: Some remarks on variations and differentials.Amer. Math. Monthly 73 (1966), No. 4, Part II (Slaught Memorial Papers), 63-76. Zbl 0141.11804, MR 0198188 |
| Reference:
|
[8] L. B. RALL: Computational Solution of Nonlinear Operator Equations.Wiley, New York, 1969. Zbl 0175.15804, MR 0240944 |
| Reference:
|
[9] L. M. GRAVES: Riemann integration and Taylor's theorem in general analysis.Trans. Amer. Math. Soc., 29 (1927), 163-177. MR 1501382 |
| Reference:
|
[10] L. M. GRATES: Topics in functional calculus.Bull. Amer. Math. Soc. 41 (1935), 641-662. MR 1563163 |
| Reference:
|
[11] T. H. HILDEBRANDT, L. M. GRAVES: Implicit functions and their differentials in general analysis.Trans. Amer. Math. Soc. 29 (1927), 127-153. MR 1501380 |
| Reference:
|
[12] M. FRÉCHET: La notion de différentielle dans l'analyse générale.Ann. Sci. Ecole Norm. Sup. 42 (1952), 293-323. |
| Reference:
|
[13] M. FRÉCHET: Sur la notion différentielle.J. Math. Pures Appl. 16 (1937), 233-250. |
| Reference:
|
[14] R. GÂTEAUX: Sur les fonctionnelles continues et les fonctionnelles analytiques.Bull. Soc. Math. France, 50 (1922), 1-21. |
| Reference:
|
[15] R. GÂTEAUX: Sur diverses questions du calcul fonctionnel.Bull. Soc. Math. France 50 (1922). |
| Reference:
|
[16] R. GÂTEAUX: Fonctions d'une infinite variable indépendantes.Bull. Soc. Math. France 47 (1919), 70-96. MR 1504784 |
| Reference:
|
[17] P. LÉVY: Leçons d'analyse fonctionnelle.Gauthier - Villars Paris, 1922. |
| Reference:
|
[18] M. KERNER: Die Differentiale in der allgemeinen Analysis.Ann. of Math. 34 (1933), 546-572. Zbl 0007.25002, MR 1503123 |
| Reference:
|
[19] M. KERNER: Zur Theorie der Impliziten Funktional Operationen.Studia Mathematica, Tom III (1931), 156-173. |
| Reference:
|
[20] M. KERNER: Sur les variations faibles et fortes d'une fonctionnelle.Annali di Matenatica Pura ed Applicata, Ser. 4, 10 (1932), 145-164. Zbl 0003.40202, MR 1553186 |
| Reference:
|
[21] E. HILLE, R. S. PHILLIPS: Functional Analysis and Semigroups.Amer. Math. Soc. Coll. Publ., Providence, 1957. Zbl 0078.10004, MR 0089373 |
| Reference:
|
[22] N. BOURBAKI: Espaces vectoriels topologiques.V. Herman, Paris, 1955. Zbl 0067.08302 |
| Reference:
|
[23] J. DIEUDONNÉ: Recent developments in the theory of locally convex vector spaces.Bull. Soc. Math. Prance 91 (1963), 227-284. |
| Reference:
|
[24] A. FRÖLICHER, W. BUCHER: Calculus in Vector Spaces without Norm.Springer - Verlag, Berlin, 1966. MR 0213869 |
| Reference:
|
[25] M. Z. HASHED: Some remarks on higher order weak differentials.- to appear. |
| Reference:
|
[26] J. KOLOMÝ: On the differentiability of mappings in functional spaces.Comment. Math. Univ. Carolinae 8 (1967), 315-329. MR 0212569 |
| Reference:
|
[27] J. KOLOMÝ, V. ZIZLER: Remarks on the differentiability of mappings in linear normed spaces.Comment. Math. Univ. Carolinae 8 (1967), 691-704. MR 0234279 |
| Reference:
|
[28] V. ZIZLER: On the differentiability of mappings in Banach spaces.Comment. Math. Univ. Carolinae 8 (1967), 415-430. Zbl 0179.19101, MR 0227772 |
| Reference:
|
[29] M. FRÉCHET: Les polynomes abstraits.Journal de Mathématiques Pures et Appliquées; ser. 9, 6.8 (1929), p. 71. MR 0070732 |
| Reference:
|
[30] A. D. MICHAL, R. S. MARTIN: Some expansions in vector spaces.J. Mathématiques Pures et Appliquées, Ser. 9, t-13 (1934), p. 69. |
| Reference:
|
[31] R. S. MARTIN: Contributions to the Theory of Functionals.(Thesis, California Institute of Technology, 1932). |
| Reference:
|
[32] I. E. HIGHBERG: A note on abstract polynomials in complex spaces.J. de Math. Pures et Appl. Ser. 9, t-16 (1937), 307-314. Zbl 0017.11804 |
| Reference:
|
[33] M. K. GAVURIN: On k-ple linear operations in Banach spaces.Dokl. Akad. Nauk SSSR 22, No. 4 (1939), 547-551. |
| Reference:
|
[34] M. K. GAVURIN: Analytic methods for the study of nonlinear functional transformations.Leningrad Gos. Univ. Uč. Zap. Ser. Mat. Nauk 19 (1950), 59-154. MR 0094730 |
| . |
