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Lipschitz Functions

open access: yesLecture Notes in Mathematics, 2019
The aim of this book is to present various facets of the theory and applications of Lipschitz functions, starting with classical and culminating with some recent results.
Stefan Cobzas   +2 more
exaly   +3 more sources

Bornologies and Locally Lipschitz Functions

open access: yesBulletin of the Australian Mathematical Society, 2014
Let hX, di be a metric space. We characterise the family of subsets of X on which each locally Lipschitz function defined on X is bounded, as well as the family of subsets on which each member of two different subfamilies consisting of uniformly locally ...
Gerald Beer
exaly   +4 more sources

Lipschitz-Type Functions on Metric Spaces

open access: yesJournal of Mathematical Analysis and Applications, 2008
In order to find metric spaces X for which the algebra Lip∗(X) of bounded Lipschitz functions on X determines the Lipschitz structure of X, we introduce the class of small-determined spaces.
Jesus A Jaramillo
exaly   +2 more sources

Locally Lipschitz Functions, Cofinal Completeness, and UC Spaces

open access: yesJournal of Mathematical Analysis and Applications, 2015
Let X, d be a metric space. We find necessary and sufficient conditions on the space for the locally Lipschitz functions to coincide with each of two more restrictive classes of locally Lipschitz functions studied by several authors: the uniformly ...
Gerald Beer, M Isabel Garrido
exaly   +2 more sources

Real-Valued Lipschitz Functions and Metric Properties of Functions

open access: yesJournal of Mathematical Analysis and Applications, 2020
The purpose of this article is to explore the very general phenomenon that a function between metric spaces has a particular metric property if and only if whenever it is followed in a composition by an arbitrary realvalued Lipschitz function, the ...
Gerald Beer, M Isabel Garrido
exaly   +2 more sources

On Lipschitz Properties of Generated Aggregation Functions

open access: yesFuzzy Sets and Systems, 2010
This article discusses Lipschitz properties of generated aggregation functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element.
Tomasa Calvo, Gleb Beliakov, Simon James
exaly   +1 more source
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Lipschitz Functions and Ekeland’s Theorem

Journal of Optimization Theory and Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gerald Beer, Jose Ceniceros
openaire   +3 more sources

Smoothing Lipschitz functions

Optimization Methods and Software, 2007
This paper describes a new approach to multivariate scattered data smoothing. It is assumed that the data are generated by a Lipschitz continuous function f, and include random noise to be filtered out. The proposed approach uses known, or estimated value of the Lipschitz constant of f, and forces the data to be consistent with the Lipschitz properties
openaire   +1 more source

Generalized Lipschitz Functions

Computational Methods and Function Theory, 2006
Lipschitz classes with variable exponents \(\text{Lip}_{\alpha(t)}\) are introduced. The exponents \({\alpha(t)}\) (called test functions) are supposed to be real-valued continuous functions defined in the right neighbourhood of zero satisfying the following conditions: \[ 1)\;{\alpha(t) = \alpha + o(1)},\;\alpha\in {\mathbb R};\quad 2) \;\int_{0}^{t} \
openaire   +2 more sources

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