Higher order differentiability of nonlinear operators on normed spaces. I.

Zuhair M. Nashed

Commentationes Mathematicae Universitatis Carolinae (1969)

  • Volume: 010, Issue: 3, page 509-533
  • ISSN: 0010-2628

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Nashed, Zuhair M.. "Higher order differentiability of nonlinear operators on normed spaces. I.." Commentationes Mathematicae Universitatis Carolinae 010.3 (1969): 509-533. <http://eudml.org/doc/16340>.

@article{Nashed1969,
author = {Nashed, Zuhair M.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {functional analysis},
language = {eng},
number = {3},
pages = {509-533},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Higher order differentiability of nonlinear operators on normed spaces. I.},
url = {http://eudml.org/doc/16340},
volume = {010},
year = {1969},
}

TY - JOUR
AU - Nashed, Zuhair M.
TI - Higher order differentiability of nonlinear operators on normed spaces. I.
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1969
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 010
IS - 3
SP - 509
EP - 533
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/16340
ER -

References

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  1. M. Z. NASHED, On the representation and differentiability of operators, (to appear). Zbl0249.46024MR0390766
  2. J. DIEUDONNÉ, Foundations of Modern Analysis, Academic Pres, New York, 1960. (1960) MR0120319
  3. L. A. LJUSTERNIK, V. J. SOBOLEV, Elements of Functional Analysis, Ungar, New York, 1961. (1961) MR0141967
  4. M. M. VAINBERG, Variational Methods for the Stady of Monlinear Operators, Holden - Day, San Francisco, 1964. (1964) 
  5. L. V. KANTOROVICH, G. P. AKHILOV, Functional Analysis in Normed Spaces, Pergamon Press, New York, 1964. (1964) 
  6. A. D. MICHAL, Le calcul differentiel dans les espaces de Banach, vol. 1, 2. Gauthier - Villars, Paris, 1958, 1964. (1958) Zbl0083.10901
  7. M. Z. NASHED, Some remarks on variations and differentials, Amer. Math. Monthly 73 (1966), No. 4, Part II (Slaught Memorial Papers), 63-76. (1966) Zbl0141.11804MR0198188
  8. L. B. RALL, Computational Solution of Nonlinear Operator Equations, Wiley, New York, 1969. (1969) Zbl0175.15804MR0240944
  9. L. M. GRAVES, Riemann integration and Taylor's theorem in general analysis, Trans. Amer. Math. Soc., 29 (1927), 163-177. (1927) MR1501382
  10. L. M. GRATES, Topics in functional calculus, Bull. Amer. Math. Soc. 41 (1935), 641-662. (1935) MR1563163
  11. T. H. HILDEBRANDT, L. M. GRAVES, Implicit functions and their differentials in general analysis, Trans. Amer. Math. Soc. 29 (1927), 127-153. (1927) MR1501380
  12. M. FRÉCHET, La notion de différentielle dans l'analyse générale, Ann. Sci. Ecole Norm. Sup. 42 (1952), 293-323. (1952) 
  13. M. FRÉCHET, Sur la notion différentielle, J. Math. Pures Appl. 16 (1937), 233-250. (1937) 
  14. R. GÂTEAUX, Sur les fonctionnelles continues et les fonctionnelles analytiques, Bull. Soc. Math. France, 50 (1922), 1-21. (1922) 
  15. R. GÂTEAUX, Sur diverses questions du calcul fonctionnel, Bull. Soc. Math. France 50 (1922). (1922) 
  16. R. GÂTEAUX, Fonctions d'une infinite variable indépendantes, Bull. Soc. Math. France 47 (1919), 70-96. (1919) MR1504784
  17. P. LÉVY, Leçons d'analyse fonctionnelle, Gauthier - Villars Paris, 1922. (1922) 
  18. M. KERNER, Die Differentiale in der allgemeinen Analysis, Ann. of Math. 34 (1933), 546-572. (1933) Zbl0007.25002MR1503123
  19. M. KERNER, Zur Theorie der Impliziten Funktional Operationen, Studia Mathematica, Tom III (1931), 156-173. (1931) 
  20. M. KERNER, Sur les variations faibles et fortes d'une fonctionnelle, Annali di Matenatica Pura ed Applicata, Ser. 4, 10 (1932), 145-164. (1932) Zbl0003.40202MR1553186
  21. E. HILLE, R. S. PHILLIPS, Functional Analysis and Semigroups, Amer. Math. Soc. Coll. Publ., Providence, 1957. (1957) Zbl0078.10004MR0089373
  22. N. BOURBAKI, Espaces vectoriels topologiques, V. Herman, Paris, 1955. (1955) Zbl0067.08302
  23. J. DIEUDONNÉ, Recent developments in the theory of locally convex vector spaces, Bull. Soc. Math. Prance 91 (1963), 227-284. (1963) 
  24. A. FRÖLICHER, W. BUCHER, Calculus in Vector Spaces without Norm, Springer - Verlag, Berlin, 1966. (1966) MR0213869
  25. M. Z. HASHED, 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. (1967) MR0212569
  27. J. KOLOMÝ, V. ZIZLER, Remarks on the differentiability of mappings in linear normed spaces, Comment. Math. Univ. Carolinae 8 (1967), 691-704. (1967) MR0234279
  28. V. ZIZLER, On the differentiability of mappings in Banach spaces, Comment. Math. Univ. Carolinae 8 (1967), 415-430. (1967) Zbl0179.19101MR0227772
  29. M. FRÉCHET, Les polynomes abstraits, Journal de Mathématiques Pures et Appliquées; ser. 9, 6.8 (1929), p. 71. (1929) MR0070732
  30. A. D. MICHAL, R. S. MARTIN, Some expansions in vector spaces, J. Mathématiques Pures et Appliquées, Ser. 9, t-13 (1934), p. 69. (1934) 
  31. R. S. MARTIN, Contributions to the Theory of Functionals, (Thesis, California Institute of Technology, 1932). (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. (1937) Zbl0017.11804
  33. M. K. GAVURIN, On k-ple linear operations in Banach spaces, Dokl. Akad. Nauk SSSR 22, No. 4 (1939), 547-551. (1939) 
  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. (1950) MR0094730

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