Geodesic
Fixed points of Lipschitzian semigroups in Banach spaces
Studia Mathematica, Tome 126 (1997) no. 2, pp. 101-113

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $T = {T_s: C → C: s ∈ G = [0,∞)}$ is a Lipschitzian semigroup such that $g = lim inf_{G ∋ α → ∞} inf_{G ∋ δ ≥ 0} 1/α ʃ^α_0 ∥T_{β+δ}∥^p dβ 1 + c$, where c > 0 is some constant, then there exists x ∈ C such that $T_sx = x$ for all s ∈ G.
DOI : 10.4064/sm-126-2-101-113
Keywords: Lipschitzian semigroup, fixed point, p-uniformly convex Banach space

Jarosław Górnicki 1

1 
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Jarosław Górnicki. Fixed points of Lipschitzian semigroups in Banach spaces. Studia Mathematica, Tome 126 (1997) no. 2, pp. 101-113. doi: 10.4064/sm-126-2-101-113

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