Generic differentiability of mappings and convex functions in Banach and locally convex spaces
Commentationes Mathematicae Universitatis Carolinae (1982)
- Volume: 023, Issue: 2, page 207-232
- ISSN: 0010-2628
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topLe Van Hot. "Generic differentiability of mappings and convex functions in Banach and locally convex spaces." Commentationes Mathematicae Universitatis Carolinae 023.2 (1982): 207-232. <http://eudml.org/doc/17175>.
@article{LeVanHot1982,
author = {Le Van Hot},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {generic differentiability; convex functions in Banach and locally convex spaces; Gateaux-differentiability; Fréchet-differentiability; S- differentiability; Asplund spaces},
language = {eng},
number = {2},
pages = {207-232},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Generic differentiability of mappings and convex functions in Banach and locally convex spaces},
url = {http://eudml.org/doc/17175},
volume = {023},
year = {1982},
}
TY - JOUR
AU - Le Van Hot
TI - Generic differentiability of mappings and convex functions in Banach and locally convex spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1982
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 023
IS - 2
SP - 207
EP - 232
LA - eng
KW - generic differentiability; convex functions in Banach and locally convex spaces; Gateaux-differentiability; Fréchet-differentiability; S- differentiability; Asplund spaces
UR - http://eudml.org/doc/17175
ER -
References
top- R. ANANTHARAMAN T. LEVIS J. H. M. WHITFIELD, Smoothabilily, strong smoothability and dentability in Banach spaces, Canad. Math. Bull. 24 (1981), 59-68. (1981) MR0611210
- N. ARONSZAJN, Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147-190. (1976) Zbl0342.46034MR0425608
- E. ASPLUND, Fréchet differentiability of convex functions, Acta Math. 121 (1968), 31-48. (1968) Zbl0162.17501MR0231199
- E. ASPLUND R. J. ROCKAFFELAR, Gradients of convex functions, Trans. Amer. Math. Soc. 139 (1969), 443-467. (1969) MR0240621
- J. M. BORWEIN, Weak local supportability and application to approximation, Pacific J. Math. 82 (1979), 323-338. (1979) MR0551692
- J. R. CHRISTENSEN, Topology and Borel structure, Math. Studia No. 10 North-Holland, Amsterdam 1974. (1974) Zbl0273.28001
- F. H. CLARK, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247-262. (1975) MR0367131
- J. B. COLLIER, A claas of strong differentiability spaces, Proc. Amer. Math. Soc. 53 (1975), 420-422. (1975) MR0388044
- J. DIESTEL, Geometry of Banach spaces, Lecture Notes in Math. No. 485, Springer-Verlag 1975. (1975) Zbl0307.46009MR0461094
- G. EDGAR, Meaaurability in Banach spaces, Indiana Univ. Math. J. 26 (1977), 663-677. (1977)
- I. EKELAND G. LEBOURG, Generic differentiability and perturbed optimization problems in Banach spaces, Trans. Amer. Math. Soc. 224 (1976), 193-216. (1976) MR0431253
- R. E. HUFF P. D. MORRIS, Dual spaces with the Krein-Milman property have the Radon-Nikodym property, Proc. Amer. Math. Soc. 49 (1975), 104-108. (1975) MR0361775
- KA SING LAU C. E. WEIL, Differentiability via directional derivatives, Proc. Amer. Math. Soc. 70 (1978), 11-1. (1978) MR0486354
- J. KOLOMÝ, On the differentiability of operators and convex functions, Comment. Math. Univ. Carolinae 9 (1968), 441-454. (1968) MR0238077
- M. K. KRASNOSELSKIJ P. P. ZABREJKO E. I. PUSTYLNIK P. E. SOBOLEVSKIJ, Integralnyje operatory v prostranstvach summirujemych funkcij, Moskva 1966. (1966)
- KUTATELADZE, Vypuklyje operatory, Uspechy Mat. nauk 34 (1979), 167-196. (1979)
- D. G. LARMAN R. R. PHELPS, Gâteaux differentiability of convex functions on Banach spaces, London Math. Soc. 20 (1979), 115-127. (1979) MR0545208
- G. LEBOURG, Generic differentiability of Lipschitzian functions, Trans. Amer. Math. Soc. 256 (1979), 125-144. (1979) Zbl0435.46031MR0546911
- P. MANKIEWICZ, On Lipschitz mapping between Fréchet spaces, Studia Math. 41 (1972), 225-241. (1972) MR0308724
- F. MIGNOT, Côntrol danse lea variationelles elliptiques, J. Functional Analysis 22 (2) (1976). (1976) MR0423155
- I. NAMIOKA R. R. PHELPS, Banach spaces which are Asplund spaces, Duke Math. J.-42 (1975), 735-750. (1975) MR0390721
- K. RITTER, Optimization theory in linear spaces: part III, Mathematical programming in partial ordered Banach spaces, Math. Ann. 184 (1970), 133-154. (1970) MR0258468
- H. H. SCHAEFER, Banach lattices and positive operators, Springer-Verlag, New York 1974. (1974) Zbl0296.47023MR0423039
- M. TALAGRAND, Deux examples de fonetions convexes, C.R. Acad. Sci. AB 288, No 8 (1979), A461-A464. (1979) MR0527697
- M. M. VAJNBERG, Variacionnyje metody issledovanija neline jnych operatorov, Nauka, Moskva 1956. (1956)
- S. YAMAMURO, Differential calculus in topological linear spaces, Lecture Notes in Mathematics No 374, Springer-Verlag, New York 1974. (1974) Zbl0276.58001MR0488118
- Ch. STEGALL, The duality between Asplund spaces and spaces with Radon-Nikodym property, Israel J. Math. 59 (1978), 408-412. (1978) MR0493268
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