On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions
Vora, Chandan S.
Rendiconti del Seminario Matematico della Università di Padova, Tome 50 (1973), p. 173-183 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1973-01-01
@article{RSMUP_1973__50__173_0,
     author = {Vora, Chandan S.},
     title = {On the estension of Lipschitz functions with respect to two Hilbert norms and two Lipschitz conditions},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {50},
     year = {1973},
     pages = {173-183},
     mrnumber = {500096},
     zbl = {0301.26009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1973__50__173_0}
}

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, Tome 50 (1973) pp. 173-183. http://gdmltest.u-ga.fr/item/RSMUP_1973__50__173_0/

[1] F.E. Browder, Existence and perturbation theorems for nonlinear monotone operators in Banach spaces, Bull. Amer. Math. Soc., 73 (1967), 322-327; MR 35, no. 3495. | MR 212625 | Zbl 0176.45205

[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. | MR 157289 | Zbl 0132.17401

[3] H. Debrunner - P. Flor, Ein Erweiterungssatz für monotone Mengen Arch. Math., 15 (1964), 445-447; MR 30, no. 428. | MR 170189 | Zbl 0129.09203

[4] B. Grunbaum, On a theorem of Kirzbraun, Bull. Res. Council Israel Sect. F, 7 (1957-58), 129-132; MR 21; no. 5155. | MR 106423

[5] B. Grunbaum, A generalisation of theorems of Kirszbraun and Minty, Proc. Amer. Math. Soc., 13 (1962), 812-814; MR 25, no. 6110. | MR 156179 | Zbl 0129.09202

[6] M.D. Kirszbraun, Über die zusammenziehenden and Lipschitzchen Transformationen, Fund. Math., 22 (1934), 7-10. | Zbl 0009.03904

[7] E.J. Mickle, On the extension of a transformation, Bull. Amer. Math. Soc., 55 (1949), 160-164; MR 10, no. 691. | MR 29974 | Zbl 0032.21401

[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. | MR 143006 | Zbl 0105.30901

[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. | MR 212631 | Zbl 0157.19103

[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. | MR 254575 | Zbl 0191.34603

[11] I.J. Schoenberg, On a theorem of Kirszbraun and Valentine, Amer. Math. Monthly, 60 (1953), 620-622; MR 15, no. 341. | MR 58232 | Zbl 0053.12201

[12] I.J. Schoenberg, as comunicated by Minty, Amer. J. Math., 38 (1937), 787-793, but I could not find it.

[13] S.O. Schonbeck, Extension of non linear contractions, Bull. Amer. Math. Soc., 72 (1966), 99-101; MR 37, no. 1960. | MR 226370 | Zbl 0135.17603

[14] F.A. Valentine, A Lipschitz condition preserving extension for a vector function, Amer. J. Math., 67 (1945), 83-93; MR 6, no. 203. | MR 11702 | Zbl 0061.37507

[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).