Bounded variation ≈ Bounded variation
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Generalized Scalar-on-Image Regression Models via Total Variation Open
The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this article is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense o…
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Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems Open
Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for i…
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A Godunov type scheme for a class of LWR traffic flow models with non-local flux Open
We present a Godunov type numerical scheme for a class of scalar conservation laws with non-local flux arising for example in traffic flow models. The proposed scheme delivers more accurate solutions than the widely used Lax-Friedrichs typ…
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BV Estimates in Optimal Transportation and Applications Open
In this paper we study the BV regularity for solutions of certain variational problems in Optimal Transportation. We prove that the Wasserstein projection of a measure with BV density on the set of measures with density bounded by a given …
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Total Variation Classes Beyond 1d: Minimax Rates, and the Limitations of Linear Smoothers Open
We consider the problem of estimating a function defined over $n$ locations on a $d$-dimensional grid (having all side lengths equal to $n^{1/d}$). When the function is constrained to have discrete total variation bounded by $C_n$, we deri…
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A combined total variation and bilateral filter approach for image robust super resolution Open
In this paper, we consider the image super-resolution (SR) reconstitution problem. The main goal consists of obtaining a high-resolution (HR) image from a set of low-resolution (LR) ones. For that, we propose a novel approach based on a re…
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Discontinuous sweeping process with prox-regular sets Open
In this paper, we study the well−posedness (in the sense of existence and uniqueness of a solution) of a discontinuous sweeping process involving prox-regular sets in Hilbert spaces. The variation of the moving set is controlled by a posit…
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Which special functions of bounded deformation have bounded variation? Open
Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV), but are less well understood. We discuss here the relatio…
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Regularization of Chattering Phenomena via Bounded Variation Controls Open
In the control theory, the term chattering is used to refer to fast oscillations of controls, such as an infinite number of switchings over a finite time interval. In this paper, we focus on three typical instances of chattering: the Fulle…
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Approximation properties of Szász type operators based on Charlier polynomials Open
In the present paper, we study some approximation properties of the Sz\'{a}sz type operators involving Charlier polynomials introduced by Varma and Ta\c{s}delen in 2012. First, we establish approximation in a Lipschitz type space and weigh…
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Relaxation and Integral Representation forFunctionals of Linear Growth on MetricMeasure spaces Open
This article studies an integral representation of functionals of linear growth on metric measure spaces with a doubling measure and a Poincaré inequality. Such a functional is defined via relaxation, and it defines a Radon measure on the …
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Observer Design for Unilaterally Constrained Lagrangian Systems: A Passivity-Based Approach Open
version preprint https://hal.archives-ouvertes.fr/hal-01113344
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Bezier variant of genuine-Durrmeyer type operators based on Polya distribution Open
In this paper we introduce the Bezier variant of genuine-Durrmeyer type operators having Polya basis functions. We give a global approximation theorem in terms of second order modulus of continuity, a direct approximation theorem by means …
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A note on the endpoint regularity of the discrete maximal operator Open
In this note we study the regularity properties of the discrete maximal operators at endpoint. Precisely, we show that the general discrete centered and non-centered maximal operators are bounded and continuous from $\ell ^1(\mathbb {Z})$ …
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Fast rates for empirical risk minimization over càdlàg functions with bounded sectional variation norm Open
Empirical risk minimization over classes functions that are bounded for some version of the variation norm has a long history, starting with Total Variation Denoising (Rudin et al., 1992), and has been considered by several recent articles…
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On Generalized Bounded Mocanu Variation Related to q-Derivative and Conic Regions Open
In this paper, we introduce a class of normalized analytic functions defined in the open unit disc.We study the unified class of functions with bounded Mocanu variation which map the open unit disk onto conic regions using q -derivative.We…
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A new modification of Durrmeyer type mixed hybrid operators Open
In 2008 V. Mihes¸an constructed a general class of linear positive operators generalizing the Szasz operators. In ´ this article, a Durrmeyer variant of these operators is introduced which is a method to approximate the Lebesgue integrable…
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Asymptotic development for the CLT in total variation distance Open
The aim of this paper is to study the asymptotic expansion in total variation in the central limit theorem when the law of the basic random variable is locally lower-bounded by the Lebesgue measure (or equivalently, has an absolutely conti…
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TWO-SIDED ESTIMATES OF THE LEBESGUE CONSTANTS WITH RESPECT TO VILENKIN SYSTEMS AND APPLICATIONS Open
In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums w…
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The Sharp Bounds of Hankel Determinants for the Families of Three-Leaf-Type Analytic Functions Open
The theory of univalent functions has shown strong significance in the field of mathematics. It is such a vast and fully applied topic that its applications exist in nearly every field of applied sciences such as nonlinear integrable syste…
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Durrmeyer-Type Generalization of Parametric Bernstein Operators Open
In this paper, we present a Durrmeyer type generalization of parametric Bernstein operators. Firstly, we study the approximation behaviour of these operators including a local and global approximation results and the rate of approximation …
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On the Bézier Variant of the Srivastava-Gupta Operators Open
In the present paper, we introduce the Bézier variant of the Srivastava-Gupta operators, which preserve constant as well as linear functions. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoo…
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Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation Open
This paper includes Voronovskaya type results and convergence in variation for the exponential Bernstein Kantorovich operators. The Voronovskaya type result is accompanied by a relation between the mentioned operators and suitable auxiliar…
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Confidence intervals for functions of coefficients of variationwith bounded parameter spaces in two gamma distributions Open
The problem of estimating parameters in a gamma distribution has been widely studied with respect to both theories and applications. In special cases, when the parameter space is bounded, the construction of the confidence interval based o…
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On continuity and compactness of some nonlinear operators in the spaces of functions of bounded variation Open
In this paper, we deal with one of the basic problems of the theory of autonomous superposition operators acting in the spaces of functions of bounded variation, namely the problem concerning their continuity. We basically consider autonom…
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Enhanced bounds for Riemann-Liouville fractional integrals: Novel variations of Milne inequalities Open
In this research article, we present novel extensions of Milne type inequalities to the realm of Riemann-Liouville fractional integrals. Our approach involves exploring significant functional classes, including convex functions, bounded fu…
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Uniqueness and Weak-BV Stability for $$2\times 2$$ Conservation Laws Open
Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small BV functions which are global solutions of this equation. For any small BV initial data, such global sol…
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Weak convergence of empirical copula processes indexed by functions Open
Weak convergence of the empirical copula process indexed by a class of functions is established. Two scenarios are considered in which either some smoothness of these functions or smoothness of the underlying copula function is required.\n…
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Discrete-to-continuum limits of multibody systems with bulk and surface long-range interactions Open
We study the atomistic-to-continuum limit of a class of energy functionals for crystalline materials via Gamma-convergence. We consider energy densities that may depend on interactions between all points of the lattice, and we give conditi…
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A new Ostrowski type inequality for functions whose first derivatives are of bounded variation Open
In this paper, we establish some new Ostrowski type integral inequalities for mappings whose first derivatives are of bounded variation and quadrature formula is provided