Fixed points of Lipschitzian semigroups in Banach spaces

Jarosław Górnicki

ArticleOriginal scientific text

Title

Fixed points of Lipschitzian semigroups in Banach spaces

Authors ¹

Affiliations

Department of Mathematics, Rzeszów Institute of Technology, P.O. Box 85, 35-959 Rzeszów, Poland

Abstract

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 = lim \in f_{G ∋ α \to \infty} \in f_{G ∋ δ \geq 0} \frac{1}{α} ʃ^{α}_0 ∥ 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.

Keywords

ENG

Lipschitzian semigroup, fixed point, p-uniformly convex Banach space

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Title

Fixed points of Lipschitzian semigroups in Banach spaces

Affiliations

Abstract

Keywords

Bibliography