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We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of the Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying functions...
The paper is devoted to the periodic bifurcation problems for generalizations of ordinary differential systems. The bifurcation is understood in the static sense of Krasnoselski and Zabreko. First, the conditions necessary for the given point to be bifurcation point for non autonomous generalized ordinary differential equations (based on the Kurzweil gauge type generalized integral) are proved. Then, as the main contribution, analogous results are obtained also for the nonlinear non autonomous measure...
It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the...
This article provides entropic inequalities for binomial-Poisson
distributions, derived from the two point space. They appear as local
inequalities of the M/M/∞ queue. They describe in particular the
exponential dissipation of Φ-entropies along this process. This simple
queueing process appears as a model of “constant curvature”, and plays for
the simple Poisson process the role played by the Ornstein-Uhlenbeck process
for Brownian Motion. Some of the inequalities are recovered by semi-group
...
A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order .
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation , where and are Henstock-Kurzweil integrable functions on . Results presented in this article are generalizations of the classical results for the Lebesgue integral.
Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.
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