Higher order differentiability of nonlinear operators on normed spaces. II.
Nashed, Zuhair M.
Commentationes Mathematicae Universitatis Carolinae, Tome 010 (1969), p. 535-557 / Harvested from Czech Digital Mathematics Library
Publié le : 1969-01-01
Classification:  46B99,  47-02,  47-80,  47H99,  47Hxx,  49Axx
@article{105250,
     author = {Zuhair M. Nashed},
     title = {Higher order differentiability of nonlinear operators on normed spaces. II.},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {010},
     year = {1969},
     pages = {535-557},
     zbl = {0206.14301},
     mrnumber = {0261414},
     language = {en},
     url = {http://dml.mathdoc.fr/item/105250}
}
Nashed, Zuhair M. Higher order differentiability of nonlinear operators on normed spaces. II.. Commentationes Mathematicae Universitatis Carolinae, Tome 010 (1969) pp. 535-557. http://gdmltest.u-ga.fr/item/105250/

M. Z. Nashed On the representation and differentiability of operators, (to appear). | MR 0390766 | Zbl 0249.46024

J. Dieudonné Foundations of Modern Analysis, Academic Press, New York, 1960. (1960) | MR 0120319

L. A. Liusternik; V. J. Sobolev Elements of Functional Analysis, Ungar, New York, 1961. (1961) | MR 0141967

M. M. Vainberg Variational Methods for the Study of Nonlinear Operators, Holden - Day, San Francisco, 1964. (1964) | MR 0176364 | Zbl 0122.35501

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) | Zbl 0083.10901

M. Z. Nashed Some remarks on variations and differentials, Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 63-76. (1966) | MR 0198188 | Zbl 0141.11804

L. B. Rall Computational Solution of Nonlinear Operator Equations, Wiley, New York, 1969. (1969) | MR 0240944 | Zbl 0175.15804

L. M. Graves Riemann integration and Taylor's theorem in general analysis, Trans. Amer. Math. Soc. 29 (1927), 163-177. (1927) | MR 1501382

L. M. Graves Topics in functional calculus, Bull. Amer. Math. Soc. 41 (1935), 641-662. (1935) | MR 1563163

T. H. Hildebrandt; L. M. Graves Implicit functions and their differentials in general analysis, Trans. Amer. Math. Soc. 29 (1927), 127-153. (1927) | MR 1501380

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) | MR 1504784

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) | MR 1503123 | Zbl 0007.25002

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) | MR 1553186 | Zbl 0003.40202

E. Hille; R. S. Phillips Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ., Providence, 1957. (1957) | MR 0089373 | Zbl 0078.10004

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) | MR 0213869

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) | MR 0212569

J. Kolomý; V. Zizler Remarks on the differentiability of mappings in linear normed spaces, Comment. Math. Univ. Carolinae 8 (1967), 691-704. (1967) | MR 0234279

V. Zizler On the differentiability of mappings in Banach spaces, Comment. Math. Univ. Carolinae 8 (1967), 415-430. (1967) | MR 0227772 | Zbl 0179.19101

M. Fréchet Les polynomes abstraits, Journal de Mathématiques Pures et Appliquées; ser. 9, t. 8 (1929), p. 71. (1929) | MR 0070732

A. D. Michal; R. S. Martin Some expansions in vector space, J. Mathématiques Pures et Appliquées, Ser. 9, t. 13 (1934), p. 69. (1934) | Zbl 0009.02301

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) | Zbl 0017.11804

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) | MR 0094730

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) | MR 0126146 | Zbl 0191.15003

M. Esser; O. Shisha A modified differentiation, Amer. Math. Monthly 71 (1964), 904-906. (1964) | MR 0196009 | Zbl 0136.03902

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) | Zbl 0019.31101

Ky Fan Sur quelques notions fondamentales de l'analyse générale, J. Math. Pures Appl. 21 (1942), 289-368. (1942) | MR 0009088

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) | Zbl 0099.10403

S. F. Long De Foglio La différentielle au sens d'Hadamard-Fréchet dans les espaces L vectorielles, Portug. Math. 19 (1960), 165-184. (1960) | MR 0124760

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) | MR 0124448

P. Murav'Ev A generalized derivative and its application to ordinary differential equations, Izv. Vysš. Učebn. Zaved. Matematika 1 (26), 89-100. | MR 0140627

A. M. Bruckner; J. L. Leonard Derivatives, Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 24-56. (1966) | MR 0197632 | Zbl 0138.27805

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) | MR 0160139

H. Oliver The exact Peano derivative, Trans. Amer. Math. Soc. 76 (1954), 444-456. (1954) | MR 0062207 | Zbl 0055.28505

A. Denjoy Sur l'intégration des coefficients différentiels d'ordre supérieur, Fund. Math. 25 (1935), 273-326. (1935) | Zbl 0012.34601

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) | MR 0138712

M. Z. Nashed Higher Order Differentiability of Nonlinear Operators on Normed Spaces - Part I, Comment. Math. Univ. Carolinae 10 (1969), 509-533. (1969) | MR 0261413