Browsing by Author "Eftekharinasab, Kaveh"

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Geometry via spray on Frechet manifolds
(Igor Sikorsky Kyiv Polytechnic Institute, 2023-10) Eftekharinasab, Kaveh; Ефтехарінасаб, Кавех Ахмадалі
For Frechet manifolds by employing sprays we will construct connection, linear symmetric connections on tangent and second-order tangent bundles.
On applcations of measure of noncompactness in Frechet spaces
(National Aviation University, 2019) Klyus, Iryna; Eftekharinasab, Kaveh; Клюс, Ірина Степанівна; Ефтехарінасаб, Кавех
In metric and topological vector spaces the notion of measure of noncompactness is used to associate numerical values to sets so that compact sets get zero measures and other ones obtain positive values that indicate how far they are different from compact sets. This concept was initiated by Kuratowski in the early 30s and has been defined and developed in many different ways. The indices of noncompactness can give us sufficient conditions for formulating various fixed point theorems in metric spaces. Another important application of these measurements is in the characterization of Fredholm operators in infinite-dimensional topological vector spaces. The object of this paper is to provide an appropriate criterion that establishes a connection between Lipschitz-Fredholm operators in the more general context of Fréchet spaces, the Hausdorff, and lower measures of noncompactness. Furthermore, by using an arbitrary measure of noncompactness in the sense of Banas and Goebel we obtain a fixed point theorem for Fréchet spaces.
On generalisation of Nagumo-Brezis theorem
(Igor Sikorsky Kyiv Polytechnic Institute, 2023-10) Eftekharinasab, Kaveh; Ефтехарінасаб, Кавех Ахмадалі; Horidko, Ruslana; Горідько, Руслана Володимирівна
We give a criterion for a closed subset of Frechet manifolds to be invariant under the flow defiind by a vector field on these manifolds.