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Displaying similar documents to “Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces.”

Fixed points of Lipschitzian semigroups in Banach spaces

Jarosław Górnicki (1997)

Studia Mathematica

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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 = l i m i n f G ∋ α → ∞ i n f G ∋ δ ≥ 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.