Peano path derivatives
نویسندگان
چکیده
منابع مشابه
Peano Path Derivatives
In this paper we introduce Peano path derivatives as a natural extension of the notion of path derivatives. We give a sufficient condition on a system of paths to ensure the corresponding Peano path derivative is Baire 1. As consequences, we obtain that unilateral approximate and unilateral Iapproximate Peano derivatives are Baire one. In studying generalized derivatives, one of the first quest...
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Peano differentiability is a notion of higher order differentiability in the ordinary sense. H. W. Oliver gave sufficient conditions for the mth Peano derivative to be a derivative in the ordinary sense in the case of functions of a real variable. Here we generalize this theorem to functions of several variables.
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We give a complete characterisation of the sets in which Peano derivatives of functions, which are definable in an o-minimal expansion of a real closed field, are continuously respectively Fréchet differentiable.
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The paper treats functions which are defined on closed subsets of [0, 1] and which are k times Peano differentiable. A necessary and sufficient condition is given for the existence of a k times Peano differentiable extension of such a function to [0, 1]. Several applications of the result are presented. In particular, functions defined on symmetric perfect sets are studied.
متن کاملInduced path transit function, monotone and Peano axioms
The induced path transit function J (u; v) in a graph consists of the set of all vertices lying on any induced path between the vertices u and v. A transit function J satis2es monotone axiom if x; y∈ J (u; v) implies J (x; y) ⊆ J (u; v). A transit function J is said to satisfy the Peano axiom if, for any u; v; w∈V; x∈ J (v; w), y∈ J (u; x), there is a z ∈ J (u; v) such that y∈ J (w; z). These t...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03878-1