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Transversally Lipschitz harmonic functions are Lipschitz [PDF]
Complex Variables and Elliptic Equations, 2013 Let Ω\subset\mathbb{R}^n be a bounded domain with C^\infty boundary. We show that a harmonic function in Ωthat is Lipschitz along a family of curves transversal to bΩis Lipschitz in Ω. The space of Lipschitz functions we consider is defined using the notion of a majorant which is a certain generalization of the power functions t^α ...
Sivaguru Ravisankar
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Lipschitz continuous points of functions on an interval
Examples and CounterexamplesIn this paper, we address the problem of finding functions with predetermined Lipschitz continuous points. More precisely, given A⊆[0,1], we are interested in the existence of function f:[0,1]→R which is Lipschitz continuous exactly on A.
Zhekai Shen
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McShane-Whitney extensions in constructive analysis [PDF]
Logical Methods in Computer Science, 2020 Within Bishop-style constructive mathematics we study the classical McShane-Whitney theorem on the extendability of real-valued Lipschitz functions defined on a subset of a metric space.
Iosif Petrakis
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Lipschitz symmetric functions on Banach spaces with symmetric bases
Karpatsʹkì Matematičnì Publìkacìï, 2021 We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_n ...
M.V. Martsinkiv +3 more
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CONTROLLING LIPSCHITZ FUNCTIONS [PDF]
Mathematika, 2018 Given any positive integers $m$ and $d$, we say the a sequence of points $(x_i)_{i\in I}$ in $\mathbb R^m$ is {\em Lipschitz-$d$-controlling} if one can select suitable values $y_i\; (i\in I)$ such that for every Lipschitz function $f:\mathbb R^m\rightarrow \mathbb R^d$ there exists $i$ with $|f(x_i)-y_i|<1$. We conjecture that for every $m\le d$, a
Kupavskii, Andrey +2 more
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Lipschitz differences and Lipschitz functions [PDF]
Colloquium Mathematicum, 1997 Let \(G\) be any of the groups \(R\) or \(T= R/Z\) (the circle group) and, for every \(L >0\), set \( \text{ Lip}_L(G) = \{g:G \to R\;\text{ such \;that \;} |g(x)-g(y)|\leq L |x-y|\;\forall x,y \in G\}, \;\text{ Lip}(G) = \bigcup_{L>0} \text{ Lip}_L(G)\).
Balcerzak, Marek +2 more
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Operator Lipschitz functions [PDF]
Russian Mathematical Surveys, 2016 109 pages, in ...
Aleksandrov, Aleksei, Peller, Vladimir
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Approximate tri-quadratic functional equations via Lipschitz conditions [PDF]
Mathematica Bohemica, 2017 In this paper, we consider Lipschitz conditions for tri-quadratic functional equations. We introduce a new notion similar to that of the left invariant mean and prove that a family of functions with this property can be approximated by tri-quadratic ...
Ismail Nikoufar
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Lipschitz Bernoulli Utility Functions
Mathematics of Operations Research, 2023 We obtain several variants of the classic von Neumann–Morgenstern expected utility theorem with and without the completeness axiom in which the derived Bernoulli utility functions are Lipschitz. The prize space in these results is an arbitrary separable metric space, and the utility functions are allowed to be unbounded.
Efe A. Ok, Nik Weaver
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Characterization of Lipschitz Spaces via Commutators of Maximal Function on the p-Adic Vector Space
Journal of Mathematics, 2022 In this paper, we give characterization of a p-adic version of Lipschitz spaces in terms of the boundedness of commutators of maximal function in the context of the p-adic version of Lebesgue spaces and Morrey spaces, where the symbols of the commutators
Qianjun He, Xiang Li
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