[2] J. DIEUDONNÉ:
Foundations of Modern Analysis. Academic Press, New York, 1960.
MR 0120319
[3] L. A. LIUSTERNIK, V. J. SOBOLEV:
Elements of Functional Analysis. Ungar, New York, 1961.
MR 0141967
[4] M. M. VAINBERG:
Variational Methods for the Study of Nonlinear Operators. Holden - Day, San Francisco, 1964.
MR 0176364 |
Zbl 0122.35501
[5] L. V. KANTOROVICH, G. P. AKHILOV: Functional Analysis in Normed Spaces. Pergamon Press, New York, 1964.
[6] A. D. MICHAL:
Le calcul différentiel dans les espaces de Banach. vol. 1, 2. Gauthier - Villars, Paris, 1958, 1964.
Zbl 0083.10901
[7] M. Z. NASHED:
Some remarks on variations and differentials. Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 63-76.
MR 0198188 |
Zbl 0141.11804
[8] L. B. RALL:
Computational Solution of Nonlinear Operator Equations. Wiley, New York, 1969.
MR 0240944 |
Zbl 0175.15804
[9] L. M. GRAVES:
Riemann integration and Taylor's theorem in general analysis. Trans. Amer. Math. Soc. 29 (1927), 163-177.
MR 1501382
[10] L. M. GRAVES:
Topics in functional calculus. Bull. Amer. Math. Soc. 41 (1935), 641-662.
MR 1563163
[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
[12] M. FRÉCHET: La notion de différentielle dans l'analyse générale. Ann. Sci. École Norm. Sup. 42 (1952), 293-323.
[13] M. FRÉCHET: Sur la notion différentielle. J. Math. Pures Appl. 16 (1937), 233-250.
[14] R. GÂTEAUX: Sur les fonctionnelles continues et les fonctionnelles analytiques. Bull. Soc. Math. France 50 (1922), 1-21.
[15] R. GÂTEAUX: Sur diverses questions du calcul fonctionnel. Bull. Soc. Math. France 50 (1922).
[16] R. GÂTEAUX:
Fonctions d'une infinité variable indépendantes. Bull. Soc. Math. France 47 (1919), 70-96.
MR 1504784
[17] P. LÉVY: Leçons d'analyse fonctionnelle. Gauthier - Villars, Paris. 1922.
[18] M. KERNER:
Die Differentiale in der allgemeinen Analysis. Ann. of Math. 34 (1933), 546-572.
MR 1503123 |
Zbl 0007.25002
[19] M. KERNER: Zur Theorie der impliziten Funktional-Operationen. Studia Mathematica, Tom III (1931), 156-173.
[20] M. KERNER:
Sur les variations faibles et fortes d'une fonctionnelle. Annali di Matematica Pura ed Applicata, Ser. 4, 10 (1932), 145-164.
MR 1553186 |
Zbl 0003.40202
[21] E. HILLE, R. S. PHILLIPS:
Functional Analysis and Semigroups. Amer. Math. Soc. Coll. Publ., Providence, 1957.
MR 0089373 |
Zbl 0078.10004
[22] N. BOURBAKI: Espaces vectorials topologiques, V. Herman, Paris, 1955.
[23] J. DIEUDONNÉ: Recent developments in the theory of locally convex vector spaces. Bull. Soc. Math. France 91 (1963), 227-284.
[24] A. FRÖLICHER, W. BUCHER:
Calculus in Vector Spaces without Norm. Springer - Verlag Berlin, 1966.
MR 0213869
[25] M. Z. NASHED: Some remarks on higher order weak differentials. To appear.
[26] J. KOLOMÝ:
On the differentiability of mappings in functional spaces. Comment. Math. Univ. Carolinae 8 (1967), 315-329.
MR 0212569
[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
[28] V. ZIZLER:
On the differentiability of mappings in Banach spaces. Comment. Math. Univ. Carolinae 8 (1967), 415-430.
MR 0227772 |
Zbl 0179.19101
[29] M. FRÉCHET:
Les polynomes abstraits. Journal de Mathématiques Pures et Appliquées; ser. 9, t. 8 (1929), p. 71.
MR 0070732
[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
[31] R. S. MARTIN: Contributions to the Theory of Functionals. (Thesis, California Institute of Technology, 1932).
[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
[33] M. K. GAVURIN: On k-ple linear operations in Bans ch spaces. Dokl. Akad. Nauk SSSR 32, No. 4 (1939), 547-551.
[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
[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).
[36] E. B. LEACH:
A note on inverse function theorems. Proc. Amer. Math. Soc. 12 (1961), 694-697.
MR 0126146 |
Zbl 0191.15003
[37] M. ESSER, O. SHISHA:
A modified differentiation. Amer. Math. Monthly 71 (1964), 904-906.
MR 0196009 |
Zbl 0136.03902
[38] M. Z. NASHED: On strong and uniform differentials. (to appear).
[39] M. HADAMARD: La notion de différentielle dans l'enseignement. (Scripta Univ. Ab. Bib. Hierosolymitanarum, Jerusalem, 1923).
[40] A. D. MICHAL:
Differential calculus in linear topological spaces. Proc. Nat. Acad. Sci. U. S. A. 24 (1938), 340-342.
Zbl 0019.31101
[41] Ky FAN:
Sur quelques notions fondamentales de l'analyse générale. J. Math. Pures Appl. 21 (1942), 289-368.
MR 0009088
[42] M. BALANZAT: La différentielle en les espacios matricas affines. Matem. Notae 9 (1949), 29-51; ibid. 19 (1964), 43-62.
[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
[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
[45] M. Z. NASHED: On Hadamard differentials and variable end-point problems in the calculus of variations. (to appear).
[46] G. H. SINDALOVSKII:
On a generalization of derived numbers. Izv. Akad. Nauk SSSR Ser. Mat. 24 (1960), 707-720.
MR 0124448
[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
[48] A. M. BRUCKNER, J. L. LEONARD:
Derivatives. Amer. Math. Monthly 73 (1966), No. 4, part II (Slaught Memorial Papers), 24-56.
MR 0197632 |
Zbl 0138.27805
[49] W. H. YOUNG: Taylor's Theorem. Proc. London Math. Soc. 7 (1909), 158.
[50] I. M. GELFAND, S. V. FOMIN:
Calculus of Variations. Prentice-Hall, Englewood Cliffs, N. J., 1963.
MR 0160139
[52] A. DENJOY:
Sur l'intégration des coefficients différentiels d'ordre supérieur. Fund. Math. 25 (1935), 273-326.
Zbl 0012.34601
[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.
[54] P. BUTZER:
Beziehungen zwischen den Riemannschen, Taylorschen und gewöhnlichen Ableitungen reelwertiger Funktionen. Math. Ann. 144 (1961), 275-298.
MR 0138712
[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