Let C be a closed, bounded, convex subset of a Hilbert space. Let T : C → C be a demicontinuous pseudocontraction. Then T has a fixed point. This is shown by a combination of topological and combinatorial methods.
@article{bwmeta1.element.bwnjournal-article-smv116i3p217bwm,
author = {James Moloney and Xinlong Weng},
title = {A fixed point theorem for demicontinuous pseudo-contractions in Hilbert apace},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {217-223},
zbl = {0840.47047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p217bwm}
}
Moloney, James; Weng, Xinlong. A fixed point theorem for demicontinuous pseudo-contractions in Hilbert apace. Studia Mathematica, Tome 113 (1995) pp. 217-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv116i3p217bwm/
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