Search results for "nuit"

Fixed points for Geraghty-Contractions in partial metric spaces

2015

We establish some fixed point theorems for mappings satisfying Geraghty-type contractive conditions in the setting of partial metric spaces and ordered partial metric spaces. Presented theorems extend and generalize many existing results in the literature. Examples are given showing that these results are proper extensions of the existing ones. c ©2014 All rights reserved.

Approximation by Certain Operators Linking the $$\alpha $$-Bernstein and the Genuine $$\alpha $$-Bernstein–Durrmeyer Operators

2020

This paper presents a new family of operators which constitute the link between \(\alpha \)-Bernstein operators and genuine \(\alpha \)-Bernstein–Durrmeyer operators. Some approximation results, which include local approximation and error estimation in terms of the modulus of continuity are given. Finally, a quantitative Voronovskaya type theorem is established and some Gruss type inequalities are obtained.

Harnack's inequality for p-harmonic functions via stochastic games

2013

We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipsc...

Fine properties of functions with bounded variation in Carnot-Carathéodory spaces

2019

Abstract We study properties of functions with bounded variation in Carnot-Caratheodory spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property R , we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.

Relations between natural and observable measures

2005

We give a complete description of relations between observable and natural measures in connection with invariance, ergodicity and absolute continuity.

Pełczyński space is isomorphic to the Lipschitz free space over a compact set

2019

International audience

2020

Abstract This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a C ∞ -hypersurface S without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of topological dimension 8, it has Hausdorff dimension 12 and so we use on it the Hausdorff measure H 12 . As a consequence, we show that any Lipschitz map defined on a subset of a Carnot group of Hausdorf…

Common fixed points for self mappings on compact metric spaces

2013

In this paper we obtain a result of existence of points of coincidence and of common fixed points for two self mappings on compact metric spaces satisfying a contractive condition of Suzuki type. We also present some examples to illustrate our results. Moreover, using the scalarization method of Du, we deduce a result of common fixed point in compact cone metric spaces.

Absolutely continuous functions and differentiability in Rn

2002

Abstract We relativize the notion of absolute continuity of functions in R n , due to Rado, Reichelderfer and Malý, to subsets of R n and use it to characterize functions (possibly vector valued) differentiable almost everywhere.

Principal eigenvalue of a very badly degenerate operator and applications

2007

Abstract In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator Δ ∞ u = ( D 2 u D u | D u | ) ⋅ D u | D u | . This operator arises from the optimal Lipschitz extension problem and it plays the same fundamental role in the calculus of variations of L ∞ functionals as the usual Laplacian does in the calculus of variations of L 2 functionals. Our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of Berestycki, Nirenberg and Varadhan [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operator…