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On condensing discrete dynamical systems

Valter Šeda (2000)

Mathematica Bohemica

In the paper the fundamental properties of discrete dynamical systems generated by an α -condensing mapping ( α is the Kuratowski measure of noncompactness) are studied. The results extend and deepen those obtained by M. A. Krasnosel’skij and A. V. Lusnikov in [21]. They are also applied to study a mathematical model for spreading of an infectious disease investigated by P. Takac in [35], [36].

On monotonic solutions of an integral equation of Abel type

Mohamed Abdalla Darwish (2008)

Mathematica Bohemica

We present an existence theorem for monotonic solutions of a quadratic integral equation of Abel type in C [ 0 , 1 ] . The famous Chandrasekhar’s integral equation is considered as a special case. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

On monotonic solutions of some integral equations

J. Caballero, Donal O'Regan, K. B. Sadarangani (2005)

Archivum Mathematicum

The aim of this paper is to obtain monotonic solutions of an integral equation of Urysohn-Stieltjes type in C [ 0 , 1 ] . Existence will be established with the aid of the measure of noncompactness.

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