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].
@article{bwmeta1.element.bwnjournal-article-div15i1n2bwm,
author = {Ireneusz Kubiaczyk},
title = {On a fixed point theorem for weakly sequentially continuous mapping},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {15},
year = {1995},
pages = {15-20},
zbl = {0832.47046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-div15i1n2bwm}
}
Ireneusz Kubiaczyk. On a fixed point theorem for weakly sequentially continuous mapping. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 15 (1995) pp. 15-20. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div15i1n2bwm/
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