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Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation

Dariusz Idczak (1998)

Czechoslovak Mathematical Journal

We give characterizations of the distributional derivatives D 1 , 1 , D 1 , 0 , D 0 , 1 of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.

Hurewicz scheme

Michal Staš (2008)

Acta Universitatis Carolinae. Mathematica et Physica

On vector functions of bounded convexity

Libor Veselý, Luděk Zajíček (2008)

Mathematica Bohemica

Let X be a normed linear space. We investigate properties of vector functions F : [ a , b ] X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K a b F is equal to the variation of F + ' on [ a , b ) . As an application, we give a simple alternative proof of an unpublished result of the first author, containing an estimate of convexity of a composed mapping.

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