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Related papers: Uniform Consistency of Generalized Fr\'echet Means

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A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler…

Differential Geometry · Mathematics 2010-09-23 Ricardo Gallego Torrome

With a new proof approach we prove in a more general setting the classical convergence theorem that almost everywhere convergence of measurable functions on a finite measure space implies convergence in measure. Specifically, we generalize…

General Mathematics · Mathematics 2020-05-15 Yu-Lin Chou

We illustrate the potential applications in machine learning of the Christoffel function, or more precisely, its empirical counterpart associated with a counting measure uniformly supported on a finite set of points. Firstly, we provide a…

Machine Learning · Computer Science 2019-02-08 Jean-Bernard Lasserre , Edouard Pauwels

We provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of \emph{generalized Fej\'er monotonicity} where (1) the metric can be replaced by a much more general type…

Functional Analysis · Mathematics 2025-07-15 Nicholas Pischke

The Fr\'{e}chet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fr\'{e}chet means in tropical geometry -- a piecewise linear,…

Optimization and Control · Mathematics 2026-03-20 Kamillo Ferry , Bo Lin , Carlos Améndola , Anthea Monod , Ruriko Yoshida

Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with H\"older continuous paths on $[0,T]$ ($T > 0$). Taking that equation in rough paths sense only gives local existence…

Probability · Mathematics 2019-01-16 Nicolas Marie

Finite Sample Smeariness (FSS) has been recently discovered. It means that the distribution of sample Fr\'echet means of underlying rather unsuspicious random variables can behave as if it were smeary for quite large regimes of finite…

Statistics Theory · Mathematics 2021-03-02 Benjamin Eltzner , Shayan Hundrieser , Stephan F. Huckemann

In this paper, we use the framework of mod-$\phi$ convergence to prove precise large or moderate deviations for quite general sequences of real valued random variables $(X_{n})_{n \in \mathbb{N}}$, which can be lattice or non-lattice…

Probability · Mathematics 2017-02-14 Valentin Féray , Pierre-Loïc Méliot , Ashkan Nikeghbali

Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…

Optimization and Control · Mathematics 2018-12-06 A Uderzo

Consider a piecewise affine Lipschitz map $\phi : \Omega \to \mathbb R$, where $\Omega \subset \mathbb R^d$ is an open set, and assume that $x \mapsto x + t \nabla \phi(x)$ is injective for almost every $t > 0$. In (J.-G. Liu, R.~L. Pego,…

Analysis of PDEs · Mathematics 2026-03-20 Stefano Bianchini , Luca Talamini

We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with…

Metric Geometry · Mathematics 2024-02-23 Syota Esaki , Daisuke Kazukawa , Ayato Mitsuishi

We propose a unifying framework for generalising the Wasserstein-1 metric to a discrepancy measure between nonnegative measures of different mass. This generalization inherits the convexity and computational efficiency from the…

Optimization and Control · Mathematics 2018-03-13 Bernhard Schmitzer , Benedikt Wirth

Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…

Machine Learning · Computer Science 2013-08-30 Zheng-Chu Guo , Yiming Ying

A generalized version of both rectangular metric spaces and rectangular quasi-metric spaces is known as rectangular quasi b-metric spaces (RQB-MS). In the current work, we define generalized $( \theta,\phi) $-contraction mappings and study…

Metric Geometry · Mathematics 2024-07-12 Mohamed Rossafi , Abdelkarim Kari

A method of proving local continuity of concave functions on convex set possessing the $\mu$-compactness property is presented. This method is based on a special approximation of these functions. The class of $\mu$-compact sets can be…

Functional Analysis · Mathematics 2010-06-22 M. E. Shirokov

We give (necessary and sufficient) conditions over a sequence $\left\{ f_{n}\right\} _{n=0}^{\infty}$ of functions under which every generalized Stieltjes moment problem \[ \int_{0}^{\infty} f_{n}(x)\phi(x)\mathrm{d} x=a_{n}, \ \ \…

Functional Analysis · Mathematics 2017-08-24 Ricardo Estrada , Jasson Vindas

Khintchine's theorem is a classical result from metric number theory which relates the Lebesgue measure of certain limsup sets with the convergence/divergence of naturally occurring volume sums. In this paper we ask whether an analogous…

Dynamical Systems · Mathematics 2020-07-23 Simon Baker

In this manuscript, motivated and inspired by results of Best proximity point of generalized $ F $-proximal non-self contractions, we introduce the concept of generalized $\theta-\phi-$proximal contraction and prove new best proximity…

Functional Analysis · Mathematics 2023-09-19 Mohamed Rossafi , Abdelkarim Kari

The g-convexity of functions on manifolds is a generalization of the convexity of functions on Rn. It plays an essential role in both differential geometry and non-convex optimization theory. This paper is concerned with g-convex smooth…

Differential Geometry · Mathematics 2024-09-24 Yu Wang , Ke Ye

Dini's Theorem guarantees that a monotone sequence of continuous functions converges pointwise on a compact interval to a continuous limit that converges uniformly. In this paper, we establish new theorems generalizing Dini's result by…

General Mathematics · Mathematics 2025-06-03 Riwaj Khatiwada