Fixed points of Lipschitzian semigroups in Banach spaces

Górnicki, Jarosław

Studia Mathematica, Tome 122 (1997), p. 101-113 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove the following theorem: Let p > 1 and let E be a real p-uniformly convex Banach space, and C a nonempty bounded closed convex subset of E. If $T = T_{s} : C \to C : s \in G = [0, \infty)$ is a Lipschitzian semigroup such that $g = l i m i n f_{G ∋ α \to \infty} i n f_{G ∋ δ \geq 0} 1 / α ʃ_{0}^{α} ∥ T_{β + δ} ∥^{p} d β < 1 + c$ , where c > 0 is some constant, then there exists x ∈ C such that $T_{s} x = x$ for all s ∈ G.

Publié le : 1997-01-01

Zbl 0894.47044

EUDML-ID : urn:eudml:doc:216446

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     author = {Jaros\l aw G\'ornicki},
     title = {Fixed points of Lipschitzian semigroups in Banach spaces},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {101-113},
     zbl = {0894.47044},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv126i2p101bwm}
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Górnicki, Jarosław. Fixed points of Lipschitzian semigroups in Banach spaces. Studia Mathematica, Tome 122 (1997) pp. 101-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv126i2p101bwm/

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