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1995 | 15 | 1 | 15-20
Tytuł artykułu

On a fixed point theorem for weakly sequentially continuous mapping

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Języki publikacji
Let E be a metrizable locally convex topological vector space x ∈ E, and let D be a closed convex subset of E such that x ∈ D.
In this paper we prove that the weakly sequentially continuous mapping F: D ∪ D which satisfies V̅ = c̅o̅n̅v̅({x} ∪ F(V))⇒ V is relatively weakly compact, has a fixed point.
Employing the above results we prove the existence theorem for the Cauchy problem
x'(t) = f(t,x(t)), x(0) = x₀.
As compared with the previous results of this type, in this theorem the continuity hypothesis on f is essentially weakened. Our results generalize those of [1,7,15,17].
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
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