Higher order differentiability of nonlinear operators on normed spaces. II.
Commentationes Mathematicae Universitatis Carolinae (1969)
- Volume: 010, Issue: 4, page 535-557
- ISSN: 0010-2628
Access Full Article
topHow to cite
topNashed, Zuhair M.. "Higher order differentiability of nonlinear operators on normed spaces. II.." Commentationes Mathematicae Universitatis Carolinae 010.4 (1969): 535-557. <http://eudml.org/doc/16341>.
@article{Nashed1969,
author = {Nashed, Zuhair M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
language = {eng},
number = {4},
pages = {535-557},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Higher order differentiability of nonlinear operators on normed spaces. II.},
url = {http://eudml.org/doc/16341},
volume = {010},
year = {1969},
}
TY - JOUR
AU - Nashed, Zuhair M.
TI - Higher order differentiability of nonlinear operators on normed spaces. II.
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1969
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 010
IS - 4
SP - 535
EP - 557
LA - eng
UR - http://eudml.org/doc/16341
ER -
References
top- M. Z. NASHED, On the representation and differentiability of operators, (to appear). Zbl0249.46024MR0390766
- J. DIEUDONNÉ, Foundations of Modern Analysis, Academic Press, New York, 1960. (1960) MR0120319
- L. A. LIUSTERNIK, V. J. SOBOLEV, Elements of Functional Analysis, Ungar, New York, 1961. (1961) MR0141967
- M. M. VAINBERG, Variational Methods for the Study of Nonlinear Operators, Holden - Day, San Francisco, 1964. (1964) Zbl0122.35501MR0176364
- L. V. KANTOROVICH, G. P. AKHILOV, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1964. (1964)
- A. D. MICHAL, Le calcul différentiel dans les espaces de Banach, vol. 1, 2. Gauthier - Villars, Paris, 1958, 1964. (1958) Zbl0083.10901
- M. Z. NASHED, Some remarks on variations and differentials, Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 63-76. (1966) Zbl0141.11804MR0198188
- L. B. RALL, Computational Solution of Nonlinear Operator Equations, Wiley, New York, 1969. (1969) Zbl0175.15804MR0240944
- L. M. GRAVES, Riemann integration and Taylor's theorem in general analysis, Trans. Amer. Math. Soc. 29 (1927), 163-177. (1927) MR1501382
- L. M. GRAVES, Topics in functional calculus, Bull. Amer. Math. Soc. 41 (1935), 641-662. (1935) MR1563163
- T. H. HILDEBRANDT, L. M. GRAVES, Implicit functions and their differentials in general analysis, Trans. Amer. Math. Soc. 29 (1927), 127-153. (1927) MR1501380
- M. FRÉCHET, La notion de différentielle dans l'analyse générale, Ann. Sci. École Norm. Sup. 42 (1952), 293-323. (1952)
- M. FRÉCHET, Sur la notion différentielle, J. Math. Pures Appl. 16 (1937), 233-250. (1937)
- R. GÂTEAUX, Sur les fonctionnelles continues et les fonctionnelles analytiques, Bull. Soc. Math. France 50 (1922), 1-21. (1922)
- R. GÂTEAUX, Sur diverses questions du calcul fonctionnel, Bull. Soc. Math. France 50 (1922). (1922)
- R. GÂTEAUX, Fonctions d'une infinité variable indépendantes, Bull. Soc. Math. France 47 (1919), 70-96. (1919) MR1504784
- P. LÉVY, Leçons d'analyse fonctionnelle, Gauthier - Villars, Paris. 1922. (1922)
- M. KERNER, Die Differentiale in der allgemeinen Analysis, Ann. of Math. 34 (1933), 546-572. (1933) Zbl0007.25002MR1503123
- M. KERNER, Zur Theorie der impliziten Funktional-Operationen, Studia Mathematica, Tom III (1931), 156-173. (1931)
- M. KERNER, Sur les variations faibles et fortes d'une fonctionnelle, Annali di Matematica Pura ed Applicata, Ser. 4, 10 (1932), 145-164. (1932) Zbl0003.40202MR1553186
- E. HILLE, R. S. PHILLIPS, Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ., Providence, 1957. (1957) Zbl0078.10004MR0089373
- N. BOURBAKI, Espaces vectorials topologiques, V, Herman, Paris, 1955. (1955)
- J. DIEUDONNÉ, Recent developments in the theory of locally convex vector spaces, Bull. Soc. Math. France 91 (1963), 227-284. (1963)
- A. FRÖLICHER, W. BUCHER, Calculus in Vector Spaces without Norm, Springer - Verlag Berlin, 1966. (1966) MR0213869
- M. Z. NASHED, Some remarks on higher order weak differentials, To appear.
- J. KOLOMÝ, On the differentiability of mappings in functional spaces, Comment. Math. Univ. Carolinae 8 (1967), 315-329. (1967) MR0212569
- J. KOLOMÝ, V. ZIZLER, Remarks on the differentiability of mappings in linear normed spaces, Comment. Math. Univ. Carolinae 8 (1967), 691-704. (1967) MR0234279
- V. ZIZLER, On the differentiability of mappings in Banach spaces, Comment. Math. Univ. Carolinae 8 (1967), 415-430. (1967) Zbl0179.19101MR0227772
- M. FRÉCHET, Les polynomes abstraits, Journal de Mathématiques Pures et Appliquées; ser. 9, t. 8 (1929), p. 71. (1929) MR0070732
- A. D. MICHAL, R. S. MARTIN, Some expansions in vector space, J. Mathématiques Pures et Appliquées, Ser. 9, t. 13 (1934), p. 69. (1934) Zbl0009.02301
- R. S. MARTIN, Contributions to the Theory of Functionals, (Thesis, California Institute of Technology, 1932). (1932)
- I. E. HIGHBERG, A note on abstract polynomials in complex spaces, J. de Math. Pures et Appl. Ser. 9, t. 16 (1937), 307-314. (1937) Zbl0017.11804
- M. K. GAVURIN, On k-ple linear operations in Bans ch spaces, Dokl. Akad. Nauk SSSR 32, No. 4 (1939), 547-551. (1939)
- M. K. GAVURIN, Analytic methods for the study of nonlinear functional transformations, Leningrad Gos. Univ. Uč. Zap. Ser. Mat. Nauk 19 (1950), 59-154. (1950) MR0094730
- G. PEANO, Sur la définition de la dérivée, Mathesis (2), 2 (1892), 12-14 (= Opere Scelte, V. 1, Edizioni Cremonese, Rome 1957, 210-212). (1957)
- E. B. LEACH, A note on inverse function theorems, Proc. Amer. Math. Soc. 12 (1961), 694-697. (1961) Zbl0191.15003MR0126146
- M. ESSER, O. SHISHA, A modified differentiation, Amer. Math. Monthly 71 (1964), 904-906. (1964) Zbl0136.03902MR0196009
- M. Z. NASHED, On strong and uniform differentials, (to appear).
- M. HADAMARD, La notion de différentielle dans l'enseignement, (Scripta Univ. Ab. Bib. Hierosolymitanarum, Jerusalem, 1923). (1923)
- A. D. MICHAL, Differential calculus in linear topological spaces, Proc. Nat. Acad. Sci. U. S. A. 24 (1938), 340-342. (1938) Zbl0019.31101
- Ky FAN, Sur quelques notions fondamentales de l'analyse générale, J. Math. Pures Appl. 21 (1942), 289-368. (1942) MR0009088
- M. BALANZAT, La différentielle en les espacios matricas affines, Matem. Notae 9 (1949), 29-51; ibid. 19 (1964), 43-62. (1949)
- M. BALANZAT, La différentielle d'Hadamard-Fréchet dans les espaces vectoriels topologiques, Compt. Rend. Acad. Sci. Paris 251 (1960), 2459-2461; ibid. 253 (1961), 1240-1242. (1960) Zbl0099.10403
- S. F. LONG de FOGLIO, La différentielle au sens d'Hadamard-Fréchet dans les espaces L vectorielles, Portug. Math. 19 (1960), 165-184. (1960) MR0124760
- M. Z. NASHED, On Hadamard differentials and variable end-point problems in the calculus of variations, (to appear).
- G. H. SINDALOVSKII, On a generalization of derived numbers, Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960), 707-720. (1960) MR0124448
- P. MURAV'EV, A generalized derivative and its application to ordinary differential equations, Izv. Vysš. Učebn. Zaved. Matematika 1 (26), 89-100. MR0140627
- A. M. BRUCKNER, J. L. LEONARD, Derivatives, Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 24-56. (1966) Zbl0138.27805MR0197632
- W. H. YOUNG, Taylor's Theorem, Proc. London Math. Soc. 7 (1909), 158. (1909)
- I. M. GELFAND, S. V. FOMIN, Calculus of Variations, Prentice-Hall, Englewood Cliffs, N. J., 1963. (1963) MR0160139
- H. OLIVER, The exact Peano derivative, Trans. Amer. Math. Soc. 76 (1954), 444-456. (1954) Zbl0055.28505MR0062207
- A. DENJOY, Sur l'intégration des coefficients différentiels d'ordre supérieur, Fund. Math. 25 (1935), 273-326. (1935) Zbl0012.34601
- C. de la VALLÉE POUSSIN, Sur l'approximation des fonctions d'une variable réelle et leurs dérivées par les polynomes et les suites limitées de Fourier, Bull. Acad. Royale de Belgique, (1908), 193-254. (1908)
- P. BUTZER, Beziehungen zwischen den Riemannschen, Taylorschen und gewöhnlichen Ableitungen reelwertiger Funktionen, Math. Ann. 144 (1961), 275-298. (1961) MR0138712
- M. Z. NASHED, Higher Order Differentiability of Nonlinear Operators on Normed Spaces - Part I, Comment. Math. Univ. Carolinae 10 (1969), 509-533. (1969) MR0261413
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.