The optimal form of selection principles for functions of a real variable
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In this paper, it was shown that if a sequence of functions { f j } j = 1 ∞ ⊂ X T is such that the closure in X of the set of functions that f j (t ) j = ∞ is compact for each t ∈ T and (∗) lim n → ∞ ( 1 n lim ǫsup j →∞ ν ( n, f j ) ) = 0, then there exists a subsequence of functions f j ∈ X T that converges in X pointwise on T toAbout:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2005-10-15 and is currently open access. It has received 32 citations till now. The article focuses on the topics: Separable space & Pointwise.read more
Citations
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Место и роль инновационных технологий на уроках математики
TL;DR: In this paper, the authors proposed a method to compute the probability of a given node having a negative value for a given value of 0, i.e., a node having no negative value is 0.
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Modular metric spaces, II: Application to superposition operators
TL;DR: In this paper, a metric semigroup and an abstract convex cone of functions of finite generalized variation are defined and a complete description of generators of Lipschitz continuous, bounded and some other classes of superposition Nemytskii operators mapping in these semigroups and cones is given.
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Maps of several variables of finite total variation. I. Mixed differences and the total variation
TL;DR: Chistyakov et al. as discussed by the authors studied properties of the total variation TV(f,Iab) of f on Iab introduced by the first author in [V.V.Hildebrandt, Introduction to the Theory of Integration, Academic Press, 1963] and Leonov [A.S.
ON p- -BOUNDED VARIATION
M. Hormozi,A. A. Ledari +1 more
TL;DR: In this paper, a characteriation of continuity of the p-variation function is given and the Helly's selection principle for BV (p) functions is established and a characterization of the inclusion of Waterman-Shiba classes into classes of functions with given inte-gral modulus of continuity is given.
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A pointwise selection principle for metric semigroup valued functions
TL;DR: In this paper, a pointwise selection theorem was proved for all functions from T into X, where the supremum is taken over all numbers from T such that s 1 ⩽ t 1 ⊆ s 2 ⩆ t 2 ⊽ t 2 2 ⋯ ⋽ s n ⩈ t n.
References
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Book
Convexity and optimization in Banach spaces
Viorel Barbu,Theodor Precupanu +1 more
TL;DR: In this article, the authors propose a method to solve the problem of convex control problems in Banach spaces. But this method is not suitable for functional analysis.Convex Functions and Convex Programming
Book
Theory of Functions of a Real Variable
TL;DR: For each x ∈ R the authors have defined a measure corresponding to Ix by prx, a probability measure in the sense that prx(Ω) = 1 and this amounts to the computation ∫ p(x, y; s)p(y, z, t)dy = p (x, z; s+ t).