Prox-mappings associated with a pair of Legendre conjugate functions

D. Wexler

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1973)

  • Volume: 7, Issue: R2, page 39-65
  • ISSN: 0764-583X

How to cite

top

Wexler, D.. "Prox-mappings associated with a pair of Legendre conjugate functions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 7.R2 (1973): 39-65. <http://eudml.org/doc/193243>.

@article{Wexler1973,
author = {Wexler, D.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
language = {eng},
number = {R2},
pages = {39-65},
publisher = {Dunod},
title = {Prox-mappings associated with a pair of Legendre conjugate functions},
url = {http://eudml.org/doc/193243},
volume = {7},
year = {1973},
}

TY - JOUR
AU - Wexler, D.
TI - Prox-mappings associated with a pair of Legendre conjugate functions
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1973
PB - Dunod
VL - 7
IS - R2
SP - 39
EP - 65
LA - eng
UR - http://eudml.org/doc/193243
ER -

References

top
  1. [1] H. ARIS, Condition suffisante de dérivabilité de l'application prox, Faculté des sciences de Montpellier, Travaux du séminaire d'analyse unilatérale, 1969, exposé n° 4. MR267435
  2. [2] E. ASPLUND, Averaged norms, Israël J. Math., 1967, 5, 227-233. Zbl0153.44301MR222610
  3. [3] E. ASPLUND, Positivity of duality mappings, Bull. Amer. Math. Soc, 1967, 73, 200-203. Zbl0149.36202MR206663
  4. [4] E. ASPLUND and R. T. ROCKAFELLAR, Gradients of convex functions, Trans. Amer. Math. Soc., 1969, 139, 443-467. Zbl0181.41901MR240621
  5. [5] A. BEURLING and A. E. LIVINGSTONE, A theorem on duality mappings in Banach spaces, Ark. Mat., 1962, 4, 405-411. Zbl0105.09301MR145320
  6. [6] F. E. BROWDER, On theorem of Beurling and Livingstone, Canad. J. Math., 1965, 17, 367-372. Zbl0132.10602MR176320
  7. [7] N. BOURBAKI, Intégration, Hermann, Paris, 1952 and 1956. MR84560
  8. [8] N. BOURBAKI, Espaces vectoriels topologiques, Hermann, Paris, 1953 and 1955. 
  9. [9] C. CASTAING, Proximité et mesurabilité, Faculté des sciences de Montpellier. Travaux du séminaire d'analyse unilatérale, 1968, exposé n° 1. MR259063
  10. [10] D. F. CUDIA, The geometry of Banach spaces. Smoothness, Trans. Amer. Math., Soc., 1964, 110, 284-314. Zbl0123.30701MR163143
  11. [11] M. M. DAY, Normed linear spaces, Springer, Berlin, 1958. Zbl0082.10603MR94675
  12. [12] N. DINCULEANU, Integrarea pe spatii local compacte, Editura Acad. R.S.R., Bucharest, 1965. MR190279
  13. [13] A. D. IOFFE and V. M. TIHOMIROV, Conjugacy of convex functionals and extremum problems (Russian), Uspehi mat. nauk, 23, 1968, 6, 51-116. Zbl0167.42202MR288601
  14. [14] M. A. KRASNOSEL'SKII and Ja. B. PUTICKII, Convex functions and Orlicz spaces (Russian), GIF-ML, Moskow, 1958. 
  15. [15] C. LESCARRET, Applications «prox» dans un espace de Banach, C. R. Acad. Sci., Paris, 1967, 265, 676-678. Zbl0175.15203MR230111
  16. [16] C. LESCARRET, Semicontinuité supérieure de la multi-application «prox», Faculté des sciences de Montpellier, Travaux du séminaire d'analyse unilatérale, 1969, exposé n° 5. MR259549
  17. [17] J. J. MOREAU, Proximité et dualité dans un espace hilbertien, Bul.. Soc. Math. France, 1965, 93, 273-299. Zbl0136.12101MR201952
  18. [18] J. J. MOREAU, Fonctionelles convexes, mimeographed lecture notes, Séminaire «Equations aux dérivées partielles», Collège de France, 1966. 
  19. [19] R. T. ROCKAFELLAR, Leval sets and continuity of conjugate functions, Trans. Amer. Math. Soc., 1966, 123, 46-63. Zbl0145.15802MR192318
  20. [20] R. T. ROCKAFELLAR, Conjugates and Legendre transforms of convex functions. Canad. J. Math., 1967, 19, 200-205. Zbl0145.06406MR213496
  21. [21] S. L. TROYANSKI, On locally uniformly convex and differentiable norms in certain non separable Banach spaces, Studia Math. 37, 1971, 2, 173-180. Zbl0214.12701MR306873

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.