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Peano type theorem for random fuzzy initial value problem

Marek T. Malinowski (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the random fuzzy differential equations and show their application by an example. Under suitable conditions the Peano type theorem on existence of solutions is proved. For our purposes, a notion of ε-solution is exploited.

Periodicity, almost periodicity for time scales and related functions

Chao Wang, Ravi P. Agarwal, Donal O’Regan (2016)

Nonautonomous Dynamical Systems

In this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

Pettis integration

Musiał, Kazimierz (1985)

Proceedings of the 13th Winter School on Abstract Analysis

Poincaré inequalities and dimension free concentration of measure

Nathael Gozlan (2010)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we consider Poincaré inequalities for non-euclidean metrics on ℝd. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for a large scope of concentration rate: between exponential and gaussian and beyond. We give equivalent functional forms of these Poincaré type inequalities in terms of transportation-cost inequalities and inf-convolution inequalities. Workable sufficient conditions are given...

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