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Volumn 28, Issue 2, 2003, Pages 287-320

Gâteaux differentiability of Lipschitz functions via directional derivatives

Author keywords

Directional derivative; Ggteaux differentiability; Lipschitz function; Lipschitz surface; Separable Banach space

Indexed keywords


EID: 33747170694     PISSN: 01471937     EISSN: 19301219     Source Type: Journal    
DOI: 10.14321/realanalexch.28.2.0287     Document Type: Article
Times cited : (5)

References (31)
  • 1
    • 0000749558 scopus 로고
    • Differentiability of Lipschitzian mappings between Ba-nach spaces
    • N.Aronszajn, Differentiability of Lipschitzian mappings between Ba-nach spaces, Studia Math., 57 (1976), 147-190
    • (1976) Studia Math , vol.57 , pp. 147-190
    • Aronszajn, N.1
  • 2
    • 22644449583 scopus 로고    scopus 로고
    • Partial subdifferentials. derivates and Rademacher's theorem
    • D. N. Bessis and F. H. Clarke, Partial subdifferentials, derivates and Rademacher's theorem, Trans. Amer. Math. Soc., 351 (1999), 2899-2926
    • (1999) Trans. Amer. Math. Soc , vol.351 , pp. 2899-2926
    • Bessis, D.N.1    Clarke, F.H.2
  • 3
    • 0003271387 scopus 로고    scopus 로고
    • Geometric Nonlinear Functional Analysis
    • Colloquium publications (American Mathematical Society), 48, Providence, Rhode Island
    • Y. Benyamini and J. Lindenstauss, Geometric Nonlinear Functional Analysis, Vol. 1, Colloquium publications (American Mathematical Society), 48, Providence, Rhode Island, 2000
    • (2000) , vol.1
    • Benyamini, Y.1    Lindenstauss, J.2
  • 4
    • 85032383690 scopus 로고
    • Some remarks on extreme derivates
    • A. M. Bruckner, Some remarks on extreme derivates, Canad. Math. Bull., 12 (1969), 385-388
    • (1969) Canad. Math. Bull , vol.12 , pp. 385-388
    • Bruckner, A.M.1
  • 7
    • 84966248518 scopus 로고
    • Differentiability via one-sided directional derivatives
    • M. Fabian, Differentiability via one-sided directional derivatives, Proc. Amer. Math. Soc., 82 (1981), 495-500
    • (1981) Proc. Amer. Math. Soc , vol.82 , pp. 495-500
    • Fabian, M.1
  • 9
    • 0000543372 scopus 로고
    • On intermediate differentiability of Lipschitz functions on certain Banach spaces
    • M. Fabian, D. Preiss, On intermediate differentiability of Lipschitz functions on certain Banach spaces, Proc. Amer. Math. Soc., 113 (1991), 733-740
    • (1991) Proc. Amer. Math. Soc , vol.113 , pp. 733-740
    • Fabian, M.1    Preiss, D.2
  • 10
    • 84971710301 scopus 로고
    • The smooth variational principle and generic differen-tiability
    • P. G. Georgiev, The smooth variational principle and generic differen-tiability, Bull. Austral. Math. Soc., 43 (1991), 169-175
    • (1991) Bull. Austral. Math. Soc , vol.43 , pp. 169-175
    • Georgiev, P.G.1
  • 11
    • 0011267369 scopus 로고
    • A characterization of Asplund spaces with the help of local supports of Ekeland and Lebourg
    • M. Fabian, N. V. Zhivkov, A characterization of Asplund spaces with the help of local supports of Ekeland and Lebourg, C. R. Acad. Bulgare Sci. 38 (1985), 671-674
    • (1985) C. R. Acad. Bulgare Sci , vol.38 , pp. 671-674
    • Fabian, M.1    Zhivkov, N.V.2
  • 12
    • 84855343240 scopus 로고
    • Sur l'extension du domaine de définition des fonctions d'une variable. qui laisse intacte la dérivabilité de la fonction
    • V. Jarník, Sur l'extension du domaine de définition des fonctions d'une variable, qui laisse intacte la dérivabilité de la fonction, Bulletin inter-national de l'Académie des Sciences de Boheme (1923), 1-5
    • (1923) Bulletin inter-national de l'Académie des Sciences de Boheme , pp. 1-5
    • Jarník, V.1
  • 13
    • 0043015624 scopus 로고
    • The quasi-differentiable functionals are almost every-where differentiable
    • P. Kenderov, The quasi-differentiable functionals are almost every-where differentiable, Math. and Education in Math., 2 (1974), 123-126
    • (1974) Math. and Education in Math , vol.2 , pp. 123-126
    • Kenderov, P.1
  • 14
    • 84968501340 scopus 로고
    • Differentiability via directional derivatives
    • K. S. Lau, C. E. Weil, Differentiability via directional derivatives, Proc. Amer. Math., Soc. 70 (1978), 11-17
    • (1978) Proc. Amer. Math., Soc , vol.70 , pp. 11-17
    • Lau, K.S.1    Weil, C.E.2
  • 15
    • 4243216609 scopus 로고
    • Derivatives and closed sets
    • J. Măírk, Derivatives and closed sets, Acta Math. Hungar. 43 (1984), 25-29
    • (1984) Acta Math. Hungar , vol.43 , pp. 25-29
    • Măírk, J.1
  • 17
    • 0007461738 scopus 로고
    • A simple proof of the Rademacher theo-rem
    • A. Nekvinda and L. Zajíček, A simple proof of the Rademacher theo-rem, Casopis Pěst. Mat., 113 (1988), 337-341
    • (1988) Casopis Pěst. Mat , vol.113 , pp. 337-341
    • Nekvinda, A.1    Zajíček, L.2
  • 18
    • 85032343823 scopus 로고    scopus 로고
    • Extensions of real and vector functions of one variable which preserve differentiability, Real Analysis Exchange, submitted
    • A. Nekvinda and L. Zajíček, Extensions of real and vector functions of one variable which preserve differentiability, Real Analysis Exchange, submitted
    • Nekvinda, A.1    Zajíček, L.2
  • 19
    • 0035652312 scopus 로고    scopus 로고
    • Directional derivatives of Lipschitz functions
    • D. Preiss and L. Zajíček, Directional derivatives of Lipschitz functions, Israel J. Math., 125 (2001), 1-27
    • (2001) Israel J. Math , vol.125 , pp. 1-27
    • Preiss, D.1    Zajíček, L.2
  • 21
    • 85032376268 scopus 로고
    • Extension of range of functions
    • E. J. Mc Shane, Extension of range of functions, Bull. Amer. Math. Soc., 76 (1970), 334-339
    • (1970) Bull. Amer. Math. Soc , vol.76 , pp. 334-339
    • Mc Shane, E.J.1
  • 22
    • 0025485978 scopus 로고
    • On concepts of directional differentiability
    • A. Shapiro, On concepts of directional differentiability, J. Optim. The-ory Appl., 66 (1990), 477-487
    • (1990) J. Optim. The-ory Appl , vol.66 , pp. 477-487
    • Shapiro, A.1
  • 23
    • 4243487328 scopus 로고
    • On the points of multivaluedness of metric projections in separable Banach spaces
    • L. Zajíček, On the points of multivaluedness of metric projections in separable Banach spaces, Comment. Math. Univ. Carolinae, 19 (1978), 513-523
    • (1978) Comment. Math. Univ. Carolinae , vol.19 , pp. 513-523
    • Zajíček, L.1
  • 24
    • 0000223562 scopus 로고
    • Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space
    • L. Zajíček, Differentiability of the distance function and points of multi-valuedness of the metric projection in Banach space, Czechoslovak Math. J., 33 (108) (1983), 292-308
    • (1983) Czechoslovak Math. J , vol.33 , Issue.108 , pp. 292-308
    • Zajíček, L.1
  • 25
    • 35348997717 scopus 로고
    • Fréchet differentiability. strict differentiability and subdif-ferentiability
    • L. Zajíček, Fréchet differentiability, strict differentiability and subdif-ferentiability, Czechoslovak Math.J., 41 (116) (1991), 471-489
    • (1991) Czechoslovak Math.J , vol.41 , Issue.116 , pp. 471-489
    • Zajíček, L.1
  • 26
    • 20144362972 scopus 로고    scopus 로고
    • On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function
    • L. Zajíček, On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function, Comment. Math. Univ. Carolinae, 38 (1997), 329-336
    • (1997) Comment. Math. Univ. Carolinae , vol.38 , pp. 329-336
    • Zajíček, L.1
  • 27
    • 0007380260 scopus 로고    scopus 로고
    • A note on intermediate differentiability of Lipschitz func-tions
    • L. Zajíček, A note on intermediate differentiability of Lipschitz func-tions, Comment. Math. Univ. Carolinae. 40 (1999), 795-799
    • (1999) Comment. Math. Univ. Carolinae , vol.40 , pp. 795-799
    • Zajíček, L.1
  • 28
    • 0013466310 scopus 로고    scopus 로고
    • Products of non-σ-porous sets and Foran systems
    • L. Zajíček, Products of non-σ-porous sets and Foran systems, Atti Sem. Mat. Fis. Univ. Modena, XLIV (1996), 497-505
    • (1996) Atti Sem. Mat. Fis. Univ. Modena , vol.44 , pp. 497-505
    • Zajíček, L.1
  • 29
    • 0001049856 scopus 로고
    • On the points of multiplicity of monotone operators
    • L. Zajíček, On the points of multiplicity of monotone operators, Com-ment. Math. Univ. Carolinae, 19 (1978), 179-189
    • (1978) Com-ment. Math. Univ. Carolinae , vol.19 , pp. 179-189
    • Zajíček, L.1
  • 30
    • 33746908069 scopus 로고    scopus 로고
    • Generic Gâteaux differentiability of locally Lipschitzian functions
    • (Varna, 1981)
    • N. V. Zhivkov, Generic Gâteaux differentiability of locally Lipschitzian functions, Collection: Constructive function theory '81 (Varna, 1981), 590-594
    • Collection: Constructive function theory , vol.81 , pp. 590-594
    • Zhivkov, N.V.1
  • 31
    • 0010890745 scopus 로고
    • Generic Gâteaux differentiability of directionally dif-ferentiable mappings
    • N. V. Zhivkov, Generic Gâteaux differentiability of directionally dif-ferentiable mappings, Rev. Roumaine Math. Pures Appl., 32 (1987), 179-188
    • (1987) Rev. Roumaine Math. Pures Appl , vol.32 , pp. 179-188
    • Zhivkov, N.V.1


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