Asymptotic behavior of almost-orbits of semigroups of Lipschitzian mappings in Banach spaces
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概要
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Let <I>C</I> be a nonempty closed convex subset of a uniformly convex Banach space <I>E</I>, <I>G</I> a right reversible semitopological semigroup and <I>S</I>={<I>S</I>(<I>t</I>) : <I>t</I>∈<I>G</I>} a continuous representation of <I>G</I> as Lipschitzain self-mappings on <I>C</I>. We consider the asymptoic behavior of an almost-orbit {<I>u</I>(<I>t</I>) : <I>t</I>∈<I>G</I>} of <I>S</I>={<I>S</I>(<I>t</I>) : (<I>t</I>)∈<I>G</I>}. We show that if <I>E</I> has a Fréchet differentiable norm and if lim<SUB><I>t</I></SUB> sup <I>k</I><SUB><I>t</I></SUB>{≤}1, then the closed convex set<BR>\underset{<I>s</I>∈<I>G</I>}∩\overline{<I>co</I>}{<I>u</I>(<I>t</I>) : <I>t</I>{≥}<I>s</I>}∩<I>F</I>(<I>S</I>)<BR>consists of at most one point, where <I>k</I><SUB><I>t</I></SUB> is the Lipschitzian constant of <I>S</I>(<I>t</I>). This result is applied to study the problem of weak convergence of the net {<I>u</I>(<I>t</I>) : <I>t</I>∈<I>G</I>}.
- 国立大学法人 東京工業大学大学院理工学研究科数学専攻の論文
国立大学法人 東京工業大学大学院理工学研究科数学専攻 | 論文
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