Displaying similar documents to “Two remarks on weak compactness”

On hyperplanes and semispaces in max–min convex geometry

Viorel Nitica, Sergeĭ Sergeev (2010)

Kybernetika

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The concept of separation by hyperplanes and halfspaces is fundamental for convex geometry and its tropical (max-plus) analogue. However, analogous separation results in max-min convex geometry are based on semispaces. This paper answers the question which semispaces are hyperplanes and when it is possible to “classically” separate by hyperplanes in max-min convex geometry.

On the existence of solutions of some second order nonlinear difference equations

Małgorzata Migda, Ewa Schmeidel, Małgorzata Zbąszyniak (2005)

Archivum Mathematicum

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We consider a second order nonlinear difference equation Δ 2 y n = a n y n + 1 + f ( n , y n , y n + 1 ) , n ∈ N . ( E ) The necessary conditions under which there exists a solution of equation (E) which can be written in the form y n + 1 = α n u n + β n v n , are given. Here u and v are two linearly independent solutions of equation Δ 2 y n = a n + 1 y n + 1 , ( lim n → ∞ α n = α < ∞ and lim n → ∞ β n = β < ∞ ) . A special case of equation (E) is also considered.