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Kannan-type cyclic contraction results in 2 -Menger space

Binayak S. Choudhury, Samir Kumar BHANDARI (2016)

Mathematica Bohemica

In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of t -norm in our theorems. In our first theorem we use a Hadzic-type t -norm. We use the minimum t -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with an example....

Large time regular solutions to the MHD equations in cylindrical domains

Wisam Alame, Wojciech M. Zajączkowski (2011)

Applicationes Mathematicae

We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in W ₂ 2 , 1 without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.

Locally admissible multi-valued maps

Mirosław Ślosarski (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.

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