This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.
@article{bwmeta1.element.bwnjournal-article-smv131i2p143bwm,
author = {Mau-Hsiang Shih and Jinn-Wen Wu},
title = {Asymptotic stability in the Schauder fixed point theorem},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {143-148},
zbl = {0924.47044},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p143bwm}
}
Shih, Mau-Hsiang; Wu, Jinn-Wen. Asymptotic stability in the Schauder fixed point theorem. Studia Mathematica, Tome 129 (1998) pp. 143-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv131i2p143bwm/
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