S. Schwabik

General integrals and extensions

Autores: 
S. Schwabik
Resumo: 
A general concept of integral is presented in the form given by S. Saks in [9]. A special subclass of integrals is introduced in such a way that the classical integrals (Newton, Riemann, Lebesgue, Perron, Kurzweil-Henstock,...) belong to it. Extensions of integrals are studied and finally the results are used for obtaining some new results on the Kurzweil-Henstock integration with emphasis to results described via the Lebesgue integral.

A converse lyapunov theorem for retarded functional differential equations

Autores: 
M. Federson, S. Schwabik
Resumo: 
We consider retarded functional differential equations and state a converse Lyapunov-type theorem for these equations by means of the theory of generalized ODEs introduced by J. Kurzweil.
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