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Title: Higher order differentiability of nonlinear operators on normed spaces. II. (English)
Author: Nashed, Zuhair M.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 10
Issue: 4
Year: 1969
Pages: 535-557
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Category: math
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MSC: 46B99
MSC: 47-02
MSC: 47-80
MSC: 47H99
MSC: 47Hxx
MSC: 49Axx
idZBL: Zbl 0206.14301
idMR: MR0261414
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Date available: 2008-06-05T20:31:10Z
Last updated: 2012-04-27
Stable URL: http://hdl.handle.net/10338.dmlcz/105250
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Related article: http://dml.cz/handle/10338.dmlcz/105248
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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 Press, New York, 1960. MR 0120319
Reference: [3] L. A. LIUSTERNIK, V. J. SOBOLEV: Elements of Functional Analysis.Ungar, New York, 1961. MR 0141967
Reference: [4] M. M. VAINBERG: Variational Methods for the Study of Nonlinear Operators.Holden - Day, San Francisco, 1964. Zbl 0122.35501, MR 0176364
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 différentiel 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. GRAVES: 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. École 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 infinité 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 Matematica 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 vectorials topologiques, V.Herman, Paris, 1955.
Reference: [23] J. DIEUDONNÉ: Recent developments in the theory of locally convex vector spaces.Bull. Soc. Math. France 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. NASHED: 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, t. 8 (1929), p. 71. MR 0070732
Reference: [30] A. D. MICHAL, R. S. MARTIN: Some expansions in vector space.J. Mathématiques Pures et Appliquées, Ser. 9, t. 13 (1934), p. 69. Zbl 0009.02301
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 Bans ch spaces.Dokl. Akad. Nauk SSSR 32, 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
Reference: [35] G. PEANO: Sur la définition de la dérivée.Mathesis (2), 2 (1892), 12-14 (= Opere Scelte, V. 1, Edizioni Cremonese, Rome 1957, 210-212).
Reference: [36] E. B. LEACH: A note on inverse function theorems.Proc. Amer. Math. Soc. 12 (1961), 694-697. Zbl 0191.15003, MR 0126146
Reference: [37] M. ESSER, O. SHISHA: A modified differentiation.Amer. Math. Monthly 71 (1964), 904-906. Zbl 0136.03902, MR 0196009
Reference: [38] M. Z. NASHED: On strong and uniform differentials.(to appear).
Reference: [39] M. HADAMARD: La notion de différentielle dans l'enseignement.(Scripta Univ. Ab. Bib. Hierosolymitanarum, Jerusalem, 1923).
Reference: [40] A. D. MICHAL: Differential calculus in linear topological spaces.Proc. Nat. Acad. Sci. U. S. A. 24 (1938), 340-342. Zbl 0019.31101
Reference: [41] Ky FAN: Sur quelques notions fondamentales de l'analyse générale.J. Math. Pures Appl. 21 (1942), 289-368. MR 0009088
Reference: [42] M. BALANZAT: La différentielle en les espacios matricas affines.Matem. Notae 9 (1949), 29-51; ibid. 19 (1964), 43-62.
Reference: [43] 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. Zbl 0099.10403
Reference: [44] S. F. LONG de FOGLIO: La différentielle au sens d'Hadamard-Fréchet dans les espaces L vectorielles.Portug. Math. 19 (1960), 165-184. MR 0124760
Reference: [45] M. Z. NASHED: On Hadamard differentials and variable end-point problems in the calculus of variations.(to appear).
Reference: [46] G. H. SINDALOVSKII: On a generalization of derived numbers.Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960), 707-720. MR 0124448
Reference: [47] P. MURAV'EV: A generalized derivative and its application to ordinary differential equations.Izv. Vysš. Učebn. Zaved. Matematika 1 (26), 89-100. MR 0140627
Reference: [48] A. M. BRUCKNER, J. L. LEONARD: Derivatives.Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 24-56. Zbl 0138.27805, MR 0197632
Reference: [49] W. H. YOUNG: Taylor's Theorem.Proc. London Math. Soc. 7 (1909), 158.
Reference: [50] I. M. GELFAND, S. V. FOMIN: Calculus of Variations.Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 0160139
Reference: [51] H. OLIVER: The exact Peano derivative.Trans. Amer. Math. Soc. 76 (1954), 444-456. Zbl 0055.28505, MR 0062207
Reference: [52] A. DENJOY: Sur l'intégration des coefficients différentiels d'ordre supérieur.Fund. Math. 25 (1935), 273-326. Zbl 0012.34601
Reference: [53] 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.
Reference: [54] P. BUTZER: Beziehungen zwischen den Riemannschen, Taylorschen und gewöhnlichen Ableitungen reelwertiger Funktionen.Math. Ann. 144 (1961), 275-298. MR 0138712
Reference: [55] M. Z. NASHED: Higher Order Differentiability of Nonlinear Operators on Normed Spaces - Part I.Comment. Math. Univ. Carolinae 10 (1969), 509-533. MR 0261413
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