On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions

Chandan S. Vora

Rendiconti del Seminario Matematico della Università di Padova (1973)

  • Volume: 50, page 173-183
  • ISSN: 0041-8994

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Vora, Chandan S.. "On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions." Rendiconti del Seminario Matematico della Università di Padova 50 (1973): 173-183. <http://eudml.org/doc/107484>.

@article{Vora1973,
author = {Vora, Chandan S.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {173-183},
publisher = {Seminario Matematico of the University of Padua},
title = {On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions},
url = {http://eudml.org/doc/107484},
volume = {50},
year = {1973},
}

TY - JOUR
AU - Vora, Chandan S.
TI - On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1973
PB - Seminario Matematico of the University of Padua
VL - 50
SP - 173
EP - 183
LA - eng
UR - http://eudml.org/doc/107484
ER -

References

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  2. [2] L. Danzer - B. Grunbaum - V. Klee, Helly's theorem and its relatives, Proc. Sympos. Pure Math., vol. 1, Amer. Math. Soc., Providence, R.I. 1963, pp. 101-180; MR 28, no. 524. Zbl0132.17401MR157289
  3. [3] H. Debrunner - P. Flor, Ein Erweiterungssatz für monotone MengenArch. Math., 15 (1964), 445-447; MR 30, no. 428. Zbl0129.09203MR170189
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  5. [5] B. Grunbaum, A generalisation of theorems of Kirszbraun and Minty, Proc. Amer. Math. Soc., 13 (1962), 812-814; MR 25, no. 6110. Zbl0129.09202MR156179
  6. [6] M.D. Kirszbraun, Über die zusammenziehenden and Lipschitzchen Transformationen, Fund. Math., 22 (1934), 7-10. Zbl0009.03904
  7. [7] E.J. Mickle, On the extension of a transformation, Bull. Amer. Math. Soc., 55 (1949), 160-164; MR 10, no. 691. Zbl0032.21401MR29974
  8. [8] G.J. Minty, On the simultaneous solution of a certain system of linear inequalities, Proc. Amer. Math. Soc. (1962), 11-12; MR 26, no. 573. Zbl0105.30901MR143006
  9. [9] G.J. Minty, On the generalisation of a direct method of the calculus of variations, Bull. Amer. Math. Soc., 73 (1967), 315-321; MR 35, no. 3501. Zbl0157.19103MR212631
  10. [10] G.J. Minty, On the extension of Lipschitz, Lipschitz Hölder continuous and monotone functions, Bull. Amer. Math. Soc., 72, no. 2 (1970), 334-339. Zbl0191.34603MR254575
  11. [11] I.J. Schoenberg, On a theorem of Kirszbraun and Valentine, Amer. Math. Monthly, 60 (1953), 620-622; MR 15, no. 341. Zbl0053.12201MR58232
  12. [12] I.J. Schoenberg, as comunicated by Minty, Amer. J. Math., 38 (1937), 787-793, but I could not find it. 
  13. [13] S.O. Schonbeck, Extension of non linear contractions, Bull. Amer. Math. Soc., 72 (1966), 99-101; MR 37, no. 1960. Zbl0135.17603MR226370
  14. [14] F.A. Valentine, A Lipschitz condition preserving extension for a vector function, Amer. J. Math., 67 (1945), 83-93; MR 6, no. 203. Zbl0061.37507MR11702
  15. [15] C.S. Vora, Fixed point theorems of symmetric product mapping of a compact A-ANR and a manifold and on Lipschitz extension theorem with respect to two Hilbert norms and two Lipschitz conditions, Indiana University, Ph. D. Thesis (in preparation). 

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