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On a fixed point theorem for weakly sequentially continuous mapping

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Kubiaczyk I.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1995

tom 15

nr 1

15-20

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].

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1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Kubiaczyk I.

1 1995

Wyniki wyszukiwania

On a fixed point theorem for weakly sequentially continuous mapping