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Notes on Lipschitz Properties of Nonlinear Scalarization Functions with Applications
Abstract and Applied Analysis, 2014 Various kinds of nonlinear scalarization functions play important roles in vector optimization. Among them, the one commonly known as the Gerstewitz function is good at scalarizing.
Fang Lu, Chun-Rong Chen
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Lusin type theorems for Radon measures [PDF]
, 2016 We add to the literature the following observation. If $\mu$ is a singular measure on $\mathbb{R}^n$ which assigns measure zero to every porous set and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lipschitz function which is non-differentiable $\mu$-a.e ...
Marchese, Andrea
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Smooth Approximation of Lipschitz Functions on Finsler Manifolds
Journal of Function Spaces and Applications, 2013 We study the smooth approximation of Lipschitz functions on Finsler manifolds, keeping control on the corresponding Lipschitz constants. We prove that, given a Lipschitz function f:M→ℝ defined on a connected, second countable Finsler manifold M, for each
M. I. Garrido +2 more
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Some Regularity Properties on Bolza problems in the Calculus of Variations
Comptes Rendus. Mathématique, 2022 The paper summarizes the main core of the last results that we obtained in [8, 4, 17] on the regularity of the value function for a Bolza problem of a one-dimensional, vectorial problem of the calculus of variations. We are concerned with a nonautonomous
Bernis, Julien +2 more
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On boundedly-convex functions on pseudo-topological vector spaces
International Journal of Mathematics and Mathematical Sciences, 2000 Notions of a boundedly convex function and of a Lipschitz-continuous function are extended to the case of functions on pseudo-topological vector spaces.
Vladimir Averbuch
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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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Fourier transforms of Dini-Lipschitz functions
International Journal of Mathematics and Mathematical Sciences, 1986 It is well known that if Lipschitz conditions of a certain order are imposed on a function f(x), then these conditions affect considerably the absolute convergence of the Fourier series and Fourier transforms of f.
M. S. Younis
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NEW INEQUALITIES ON LIPSCHITZ FUNCTIONS [PDF]
Facta Universitatis, Series: Mathematics and Informatics, 2020 In this study, some inequalities of Hermite Hadamard type obtained for p-convex functions are given for Lipschitz mappings. Also, some applications for special means have been given.
İşcan, İmdat +2 more
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Essentially Smooth Lipschitz Functions
Journal of Functional Analysis, 1997 The authors observe fundamental questions regarding the differentiability structure of locally Lipschitz functions defined on Banach spaces. So the following 3 significant properties are discussed: (P1) \(D\)-representability, which means Gâteaux-differentiability on a dense subset \(D\) of the domain and the description of the Clarke subdifferential ...
Borwein, Jonathan M., Moors, Warren B.
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Lipschitz Continuity of Convex Functions [PDF]
Applied Mathematics & Optimization, 2020 17 ...
Bao Tran Nguyen, Pham Duy Khanh
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