Contraction Property of the Operator of Integration
Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 367-369
Voir la notice de l'article provenant de la source Cambridge University Press
It is shown that the operator of integration Fy(x) = ∫x 0y(t) dt defined on the space C(—∞, ∞) of all continuous real valued functions on (—∞, ∞) is a contraction relative to a certain family of seminorms generating the topology of uniform convergence on compacta. However, as a contrast to this it is proved that F is not contractive with respect to any metric on C(—∞, ∞) inducing the above topology on C(—∞, ∞).
Contraction Property of the Operator of Integration. Canadian mathematical bulletin, Tome 18 (1975) no. 3, pp. 367-369. doi: 10.4153/CMB-1975-066-0
@misc{10_4153_CMB_1975_066_0,
title = {Contraction {Property} of the {Operator} of {Integration}},
journal = {Canadian mathematical bulletin},
pages = {367--369},
year = {1975},
volume = {18},
number = {3},
doi = {10.4153/CMB-1975-066-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-066-0/}
}
[1] 1. Janos, L., Topological homo the ties on compact Hausdorff spaces, Proceedings of the A. M.S. Vol. 21, No. 3, June 1969. pp. 562-568. Google Scholar
[2] 2. Chu, Sherwood C. and Diaz, J. B., A fixed point theorem for “in large” application of the contraction principle, Atti della Accademia delle Scienze di Torino Vol. 99,1964-65. pp. 351-363. Google Scholar
[3] 3. Meyers, Ph. R., A converse to Banach’s contraction theorem, J. Res. Nat. Bur. Standards Ser. B71B, 1967. pp. 73-76. Google Scholar
Cité par Sources :