Minimal displacement of points under weakly inward pseudo-lipschitzian mappings
Reich, Simeon
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975), p. 40-44 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

Sia C un sottinsieme limitato, chiuso e convesso di uno spazio di Banach (E,∥) e sia T una trasformazione continua, debolmente interna pseudo-lipschitziana. In questa Nota si considera inf{|x-Tx|:x∈C}. T appartiene a questa classe di rappresentazione se e soltanto se T-I (I indica l'identità) è un generatore fortemente continuo di semigruppo non lineare di C.

Publié le : 1975-07-01
@article{RLINA_1975_8_59_1-2_40_0,
     author = {Simeon Reich},
     title = {Minimal displacement of points under weakly inward pseudo-lipschitzian mappings},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
     volume = {59},
     year = {1975},
     pages = {40-44},
     zbl = {0347.47039},
     mrnumber = {0451058},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLINA_1975_8_59_1-2_40_0}
}

Reich, Simeon. Minimal displacement of points under weakly inward pseudo-lipschitzian mappings. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 59 (1975) pp. 40-44. http://gdmltest.u-ga.fr/item/RLINA_1975_8_59_1-2_40_0/

[1] Bony, J.-M. (1969) - Principe du maximum, inégalité de Harnack et unicité d'un problème de Cauchy pour les opérateurs elliptiques dégénérés, «Ann. Inst. Fourier Grenoble», 19, 277-304. | MR 262881 | Zbl 0176.09703

[2] Browder, F. E. (1967) - Nonlinear mappings of nonexpansive and accretive type in Banach spaces, «Bull. Amer. Math. Soc.», 73, 875-882. | MR 232255 | Zbl 0176.45302

[3] Caristi, J. - Fixed point theorems for mappings satisfying inwardness conditions, to appear. | MR 394329

[4] Crandall, M. G. (1972) - A generalization of Peano's existence theorem and flow invariance, «Proc. Amer. Math. Soc.», 36, 151-155. | MR 306586 | Zbl 0271.34084

[5] Deimling, K. (1974) - Zeros of accretive operators, «Manuscripta Math.», 13, 365-374. | MR 350538 | Zbl 0288.47047

[6] Goebel, K. (1973) - On the minimal displacement of points under lipschitzian mappings, «Pacific J. Math.», 45, 151-163. | MR 328708 | Zbl 0265.47046

[7] Halpern, B. R. and Bergman, G. M. (1968) - A fixed point theorem for inward and outward maps, «Trans. Amer. Math. Soc.», 130, 353-358, | MR 221345 | Zbl 0153.45602

[8] Holmes, R. B. (1972) - A Course on Optimization and Best Approximation, «Lecture Notes in Mathematics», 257, Springer, Berlin. | MR 420367 | Zbl 0235.41016

[9] Kato, T. (1967) - Nonlinear semigroups and evolution equations, «J. Math. Soc. Japan», 19, 508-520. | MR 226230 | Zbl 0163.38303

[10] Martin, R. H., Jr. (1970) - The logarithmic derivative and equations of evolution in a Banach space, «J. Math. Soc. Japan», 22, 411-429. | MR 298467 | Zbl 0199.47003

[11] Martin, R. H., Jr. (1973) - Differential equations on closed subsets of a Banach space, «Trans. Amer. Math. Soc.», 179, 399-414. | MR 318991

[12] Reich, S. (1973) - On the fixed point theorems of Banach and Schauder, doctoral dissertation, The Technion—Israel Institute of Technology, Haifa. (In Hebrew, with an English summary. An abstract appeared in «Dissertation Abstracts International», 34 (11), 1974).

[13J Reich, S. - On fixed point theorems obtained from existence theorems for differential equations, «J. Math. Anal. Appl.», to appear. | MR 402554