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On a fixed point theorem for weakly sequentially continuous mapping

Ireneusz Kubiaczyk (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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...

On a nonlocal problem for fractional integrodifferential inclusions in Banach spaces

Zuomao Yan (2011)

Annales Polonici Mathematici

This paper investigates a class of fractional functional integrodifferential inclusions with nonlocal conditions in Banach spaces. The existence of mild solutions of these inclusions is determined under mixed continuity and Carathéodory conditions by using strongly continuous operator semigroups and Bohnenblust-Karlin's fixed point theorem.

On a Theorem of Mierczyński

Gerd Herzog (1998)

Colloquium Mathematicae

We prove that the initial value problem x’(t) = f(t,x(t)), is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.

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