Reich: Minimal displacement of points under weakly inward pseudo-lipschitzian mappings

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 Serie 8 59 (1975), fasc. n.1-2, p. 40-44, (English)
pdf (511 Kb), djvu (656 Kb). | MR 0451058 | Zbl 0347.47039

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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 $\inf \{ |x - Tx| : x \in C \}$. $T$ 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.

Referenze Bibliografiche

[1] J.-M. BONY (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. | fulltext EuDML | MR 262881 | Zbl 0176.09703

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

[3] J. CARISTI - Fixed point theorems for mappings satisfying inwardness conditions, to appear. | fulltext (doi) | MR 394329

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

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

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

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

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

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

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

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

[12] S. REICH (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 S. REICH - On fixed point theorems obtained from existence theorems for differential equations, «J. Math. Anal. Appl.», to appear. | fulltext (doi) | MR 402554

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Referenze Bibliografiche